As someone who first got intrigued by choke when ice fisherman was printed. Here is my analysis and view on choke.
The easy way to explain how choke work is to say there are two goals. The first goal is to lock or soft lock your opponent from his resources. After the first goal is achieved you use Valar to wipe the board and from that moment on you are completely dominating the flow of the game. So lock and wipe is the main strategy.
NPE is a problem of most of the control decks for the way they play. They usually try to react to every play the opponent makes to make sure they have complete control at the end. Now with choke, this control type is completely different from the others. Where you want to react with the others you want to take action with choke. As a choke player you should aim to always be the first player - probably everyone has figured this to get their -1 gold to hit opponent faster, but it has other uses as well. Going first makes sure that you get to hit with your marauders before they do anything. It also does something which is very vital for the deck, which is your carrion bird. As Greyjoy doesn't have as much spot control, opposing carrion bird and/or season can ruin your game at times, so it becomes more important to get your own bird or marauder to hit first. Now this is something that you should be looking at when you are opposing a choke deck, go first to restrict their choke and choices.
1) Pure choke: I feel this is the most common choke there is currently. This deck is hellbent on choking opponent from all of his gold and nothing more nothing less. Now this deck is good at what it is doing, but most of the times it is doing way too much for no benefit (having 2 fisherman and cragorn on the table while your opponent isn't even counting gold). This can be fixed by also adding game closing cards - the Asha that was meantioned in the article linked is a good example of how to get your pure choke to close games faster. Sometimes I still see versions of this deck that don't have game enders and it just seems odd.
2) Maester choke: I rarely see this in reports and it takes a completely new style of turn for choke. It has more control elements and is more versatile, but as a weak spot the greyjoy maesters are weak and highly flammable. Basically this type sacrifices more of its pure choke to have more answers to different cards your opponent can play.
3) Cancel choke: This is a type I haven't seen in any reports but I feel should be more popular. With added cancel the choke can disturb the opponent on more levels than just gold and stop their attempts to get out of the lock. Both of these themes strengthens each other, but to achieve this you have to drop some of the pure choke cards to add in cancel. This is probably also the most purest control version of the choke as it has added reactive elements from the cancel.
4) Aggro choke: This can be either a purely aggro with choke or rush with added choke. I heard one of these decks did well in Stachleck last year and I wonder why I don't see these decks either. Now that Greyjoy has gotten more renown and nobles I can see it very viable to have a rush deck with added choke to slow your opponent down while your characters are having fun with renown and saves.
The good and bad opponents:
I will now list the good and bad match-ups for choke, if you have any questions why something is on one list do ask since this post will become too huge if I write an explanation of why some deck is a good and why bad.
Bad: Stark siege, Stark shadows, Baratheon rush, Maesters especially the ones who like to rush, KotHH builds, Targaryen summer, Power behind the throne, mirror match
Good: Martell, Lannister kneel, most non-Stark Shadows Builds, wildlings, any other slow control build.
Common elements in choke decks:
1) FearblockRBD: This is a plot combo that will be the choke decks strength and weakness. This is completely a meta choice as it hurts you more against the decks you are weak to already and makes you only better against decks that you were doing good. The thing is, if you can't drop that fear first turn then you have to save it to be played after you have gotten your lock and used valar. Its never a dead plot, but I would still give more consideration on choosing your restricted card. Blockade (which is good card) is something that I cannot understand even when comboed with fear. Ok so you are playing a choke deck and you often get your opponent in a situation where they are counting 1-2 gold and then you decide to play blockade, you are taking from them only slight amount of gold and taking a lot more from yourself while doing this which generally isn't worth it. Rule by decree I have nothing bad to say, works well in this combo and even out of it. Anyone who has played this game for long will know this plot order and personally I have mostly stopped using this in my choke decks as I feel it takes flexibility from me and doesn't help against bad matchups.
2) Wintertime Marauders: This is still the single most powerful Greyjoy card there is. It will work in any situation and do anything you want it to do as long as you can keep it winter.
3) Cragorn: Unless your deck is running a very heavy resource base I wouldn't slide him into a choke deck especially if you already have the fishermen. With 2 gold you are gaining 1 gold and your opponent is losing 1 not a good deal to me when there is already a 1 cost character that can do it.
4) Ice fishermen: This is another card that isn't completely vital for a choke, but still gets slided into nearly every choke. The problem with these guys is that they don't do anything without winter. When its winter you should not look at their ability to be "steal one gold" you should look it like "your opponent will play one or two high gold card(s) before you get to use him" and the better your deck can use this to your advantage the more likely it should be for you to run these.
5) Burned and pillaged: This is the card that is the key for burn. For most decks this will be the card that will break them. Unfortunately its completely useless against KotHH decks as those decks only suffer for the initiative loss. When the environment is heavy on KotHH I would slide these out and possibly add support of the kingdom if the deck isn't already running it.
6) River blockade: This card is very very versatile and can be seen in decks with no other choke elements in it. Its power comes from the fact that at first it is resource denial and when your opponent doesn't have reducers any more it becomes strong location control. Your opponent usually can trigger the location he wants to trigger, but it comes with a heavy price.
The only card on the common elements list what I can see being nearly too powerful is marauders as it is one of the best toolbox cards in the game. Seasons on themselves are really problematic, in choke I get access to repeatable card discard (agenda) draw (Samwell Tarly) income denial (white raven). All of the season elements in choke are very powerful and easy to run. Mostly I feel that the untouchability of the white raven (also black, but not for choke) is what drives these decks so well. The decks core is well protected by itself without need of other cards.
Why did I do this analysis? to give more knowledge of the choke type. To help see what it uses, how it plays and to take observations on how to fight it. I did this as well to show that there is a lot of room which choke decks should explore instead of going the safest way and keeping their decks pure choke and at states where the deck was at 1 year ago when burned & pillaged was printed (like the pure choke). Yes choke is strong deck type I agree with that, but there are many ways to fight it and there also are many ways to evolve choke to deal with new threats but it will also gain new weaknesses while doing so.
Now for Aeron Damphair, I cannot see this card entering any of my choke decks. The problem with him is that most of the times he will be on on turns 2-4 and starts to generate draw in turns 3-5. With kings of winter my agenda is usually on from the turn 1-2 and stars working on my opponent in turns 2-3. Thanks for the season being the odd mechanic with build in great draw engine, I can get draw faster than I could with Damphair. Samwell also has a great psychological advantage as well. Will my opponent give me cards to try and remove my season with his own carrion bird? As winter choke gets its draw from easier choice and has a good agenda I cannot see Damphair breaking it. Only thing that I can see is new subtype of choke which will use either heavy saves or holy characters and wants this to make it run more smoothly, but it will not make that deck broken without other new cards.