Gamist to me means a desire to have explicit rules, numbers that can be crunched, and calculations that can be made in order for someone to plan out how to gain an advantage using the rules as written.
A lot of the best eurogames (strategy games) are very gamist, in that everyone knows the rules, everyone knows the winning conditions, and everyone is free to come up with a strategy to attain those goals. It is important that there are mechanics that can be manipulated, so that it isn't a game of luck or diplomacy.
I don't think of "gamist" as a perjorative. It is similar to min-maxing or optimizing. 4E has a very "gamist" approach to its tactical combat. I'd say that 4E is the most gamist version of D&D available, and that is a great strength of the game.
When I play eurogames, I really enjoy strategizing. A lot if miniatures games are also very "gamist".
Roleplaying games also allow for some other sources of enjoyment, such as people who like to immerse themselves in the game world. Its possible to have a lot of fun roleplaying without caring about the mechanics or trying to use the rules to gain an advantage... the thrill is in the imaginary world. I might call these people "immersionists"
There are also some people who don't give a crap about the imaginary world or the rules of the game, they just like socializing with friends, drinking beer, eating pretzels, and enjoying the company. Since these people like socializing I will call them "Socialists".
There are several other things that people can enjoy when roleplaying... arguing with other people (rules-lawyering), or perhaps the escapist fantasy aspects... I don't think there is a right or wrong way to play, but it is good to know what you like and what your friends like so that you can make sure you accomodate them.
As a gamist, I get pretty frustrated if the GM is fudging dice rolls or changing the target numbers after-the-fact. I like to be able to consider things like "My character is down to 5HP, if I keep fighting there is a 20% chance I'll die, on the other hand, if I surrender I can probably talk my way out of the situation... thus I'll surrender." Knowing the target numbers and stats of my opponents helps inform my decision on how to play the character, and I feel good for having made decisions that take the math into account.