I prefer #1 because it is more direct & efficient, and it is a very commonly used structure so people will be more naturally able to understand you without needing to think about it. Just fix the typo, say "video games always distract" or say "playing video games always distracts".
However, if you really want to emphasise the "forgetfulness" then you will need to use that word, which is in #2 and #3 but not #1. So it's all about what message exactly you wish to convey.
Here are corrected versions of those sentences, with notes:
1) Video games always distract him from his homework. -- This is very concise and natural.
2) He is always distracted by video games and forgets about his homework. -- This is more detailed. It is technically fine, but only necessary if you wish to emphasise the act of forgetting, otherwise it's inefficient / unnecessarily longwinded.
3) Video games are always a distraction to him - they make him forget his homework. -- This is like #2. It's unnecessarily longwinded / inefficient unless you wish to explicitly refer to the act of forgetting, in which case this is then fine.