It means this person thinks that they could play video games as their job. They say they may "go pro" which means to become a professional in that subject, someone who is payed to do it.

Similar to what Krystal said, the person is using the filler ‘like’ in their sentences. Fillers don’t create a meaning but are placed by the speaker when they’re thinking. So when they’re saying ‘probably like go to a pro life’ They mean : I will probably become a professional.

If you delete all the "like" words in this sentence, this person will make much more sense. In this situation, "like" does not mean anything. It is like saying "uhm" or "uh" to give yourself time to think. Exception: In your conversation, "games like that" is the only "like" that means "similar to; of this kind". "Probably (like) go to a pro life" means "become a professional."