Runebound is certainly a race to the end, but not really the same way as Talisman. There's isn't much direct interaction between players, unless they go out of their way to bump into each other. One player reaching for the next colour grade certainly indicates he is making progress and should act as a kick in the nards for everyone else to get moving, but it doesn't mean the other players are completely screwed just because he got there first.
On the other hand, bad luck can screw a player and keep him down regardless of what any other players are doing.
The "race" element doesn't really kick in until someone breaks red challenges, in my experience. At that point, anyone else who's hoping to win really wants to be hitting red themselves within a turn or two. Before that point, there's a steady build up as you move from green to yellow to blue, but for the most part everyone is just doing their own thing and seeing what they find.
Personally, the thing I enjoy about Runebound is the story that unfolds through event cards and through the circumstantial adventures we watch our heroes go through. Laughing about how one hero always gets a particular type of encounter, gloating over our own good fortune (or bemoaning our own bad fortune.) It's all in good fun, of course. It hardly even matters who wins, and several of our games have, in fact, ended without us getting to red challenges. We call the game on time and usually make some desperate final attacks, throwing our unprepared heroes upon red (or sometimes blue) challenges just to see how many rounds we can go with whatever turns up.
It's a great game, but it can seem somewhat "aimless" at times. That might sound like a bad thing at first, but it lends the game a sense of wanderlust you just don't find in games that more focused on a specific goal.