Modern usage:
cinematic
adj : of or pertaining to or characteristic of the cinema
Source: WordNet® 1.6, © 1997 Princeton University
In the games, the word "cinematic" is usually used to describe things that are "movie-realistic", that is, things that happen in movies but are not likely to happen in real life, but are still credible - or, sometimes, they can be clearly over the top, as long as the internal realism stays.
For example, a historical/realistic role playing game campaign would use as much actual history material or realistic details, while a fantasy/cinematic campaign would have things that would require a special effects budget for flashy spells and explosions... and heroes do things that require certain amounts of wiring.