Good games give me the same feeling as reading a good fictional novel: I get transported into the universe, following the character or whatever action is unfolding.
More generally, games give the player a goal to achieve, whether that's winning over others, cooperating with others, completing a campaign, collecting a bunch of goodies (or all the goodies), relaxing and enjoying scenery, crafting min-maxed playthroughs, or trying over and over again to beat a level.
Being focused on this goal can help keep your mind off of whatever is troubling you in the present.