For me, what makes great game sagas great, is the storyline, character development, new release tension etc. I'm thinking games like the Half-Life series, and Metal Gear Solid. These games developed with an in-depth story in mind are always going to be held in high acclaim by regular gamers.
What I find difficult to grasp with movies made straight from games is they prohibit further development of that story, leaving a franchise where game after game is released with no real progression. All 3 films and their playable counterparts you've mentioned suffer from this. Sure, a Tomb Raider game is fun once in a while, but you can't connect with it.
Can the experience of any of these games really be transferred? I don't think (yet) that it can be ported to the silver screen, however I can't predict how this could be changed.