"Yeah, up up, down down, left right, left right, B A doesn't work in Quake 3. So much for memorization."
You're obviously forgetting to hit start, duh.
"though there clearly is some benefit to prior video game experiences help you learn new video games."
If as you play more and more video games, you actually pay attention to the design of the games as opposed to just blindly playing through the game, you will develop a very keen '6th sense' in video games and it has a lot to do with the fact that you've learned how to get inside the head of the developers who make games. You get a very good sense for the inherent pacing that a lot of games tend to have, so the more games you play, the harder it will be to surprise you. You'll feel a lull in combat for instance and just have that sense that you may be about to hit a sub-boss fight or a big enemy wave.
An excellent example was when me and a few friends were playing through Borderlands and we were coming up on the Roid Rage Psycho boss. Before you get to him there's a hall you have to go down that gets oddly quiet and at the end you have to drop down off a ledge. We all just looked at each other and all remarked that there just "HAD to be a boss fight coming up." Sure enough the Psycho spawned in once we all got down into the boss arena.
Another good example in the opposite spectrum is the opening Marine level of AVP 2. We were so used to playing FPSs that pretty much had you running and gunning from level 1 that when this game came along presented us with an opening level that didn't have any shooting whatsoever, it had a lot of us jumping at shadows and actually getting shaken up by the atmosphere soley because the game was going against everything other video games had taught us pacing wise.
Playing Brain Age might not develop any new thinking skills like playing a really involved RTS would, but much like doing a daily crossword puzzle, it will help to keep your brain from essentially atrophying.