A game is deterministic if the resolution of player actions leads to completely predictable outcomes. It is indeterministic to one degree or another if actions lead to potentially chaotic outcomes. Chess is an example of a determinist game: the rules allow for no variation of outcome and there are no physical factors involved. Football, on the other hand, is an indeterminist game: players cannot reliably kick the ball exactly the same way each time, and the small variations of that action lead to chaotic outcomes.
A sense of indeterminism, or luck, often makes a game exciting. Players like to sense that there is always a chance that they will win, that the right card will land or a ball will make a lucky bounce. However too much indeterminism (such as in Snakes and Ladders) removes all sense of agency from the game, and that's rarely fun.
Determinism in Programming
Programmers mean something slightly different when discussing deteminism. A game engine like Quake may well be determinist in terms of replicating the results of player action faithfully, but to the player it may feel indeterminist because their execution of that action may be slightly wrong. So although the game is not random, to player it feels a little like it is.
To a programmer, the question of determinism is all about how the game engine behaves. To the game designer, it is about how it is perceived to behave.