There are plenty of reasons why gamers optimize, and "treating like a video game to be won" is but one possibility.
No, they also don't. Trust me, people were power gaming and optimizing before there was an internet. I can personally attest to that. MMO culture may have partially stemmed from that.
Metagaming is completely different from optimizing. Sure, a Venn diagram will have some overlap, but so would "people who believe dice superstitions" or "people who use names from Tolkien" - it's not meaningful. Metagaming is using knowledge your character would not have to do better. I personally am against it, but I know some of our regular posters don't even see a problem with it. Optimization is using mastery of the system in order to improve your character or your party. (And for completeness, minmaxers are a subset of that who try to minimize their weaknesses while maximizing their character's strengths.)
I have no beef with optimization as long as everyone at the table is having fun. Which often includes everyone optimizing, or the optimizers going for more support characters whom make everyone else shine and get spotlight.
But both metagaming and optimization long predate MMOs.