This is slang. It's not referring to a sport or game. It refers to sex. "Pull out" is a method people use during sex to prevent pregnancies (even though this method is highly ineffective). It involves a male removing ("pulling out") his penis from inside the female before he ejaculates. "Game" essentially means "skill/ability". So "she knows my pull out game strong" means "she knows that I'm very capable of removing my penis from inside her before I ejaculate".

It's missing "is". Even though it's in a tweet, there's still space fr one more word! "I play jenga on the first date so she knows my pullout game (is) strong." I guess you know the game jenga. I agree with Cherry - there's a sexual innuendo here.

It is clearly wrong. It is either copied incorrectly, or written by a non-native speaker. At the very least, there should be an 'is' before 'strong'. a 'pullout game' may be some sort of jargon particular to some sport. It's not one I am familiar with. It would help if you gave some context.