Video games are not sinful just because Jesus and Mary didn't have them. If that was the case, then computers and TVs and any other kind of technology, and even hobbies like drawing and writing would be sinful. You can't judge everything by whether Jesus did it or not.
If they were already baptized once, that is enough. It doesn't matter if they remember it or not-baptism invites you into God's "family" and does not need to be done more than once.
Confessing their sins is always a good idea, though.
I agree with you over all, however I do not agree that all baptisms are the same.
For example, a baby being baptized I do not feel is the one that matters. It may be a symbol of the parents will to give the child over to God, but that takes free will out of the picture.
I believe the baptism that "counts" is the one done by ones own free will of understanding the choice they are making and the world they are laying down for that choice. (To say in action, I die to my will to make way for God's)
That said, I do not believe even the act of baptism (in earthly water) saves as only the blood shed by Jesus saves. Baptism (in water) is simply the symbolic act to show the world that choice that it (the world) no longer has right/authority over you (even if the reality if being free from the world is still long ways off) still important to do, but not the end all be all of salvation.
As far as video games being sin.... let each person be convinced in their own minds.
Jesus did not play video games, but He most certainly DID allow Himself entertainment and fun. We already know He attended parties and festivals through whst is said in the Bible. Are we to think that He sat in a corner unhappy and bored?
Yes, He didnt sin in His entertainment, but I doubt seriously Jesus did nothing but walk around bored and miserable.
Jesus was a kid, as a kid He no doubt played like a kid. Being without sin however meant that though He played like a child, He obeyed His earthly parents even though they were imperfect.
Even when the children were climbing on Jesus. He didnt say "calm down and do not be children".
Video games are no worse or better than anything else in this world. It is simply were they or anything hold a place in our heart. If we put its value above God. (If you have 8 hours of free time a day, spend 7.5 hours playing video games or whatever else... then 20 mins doing something else then 10 or less in the word or even thinking 9r meditating on the Father... you have to ask what is it you truly value in this world and do you (honestly) put it above God.
If you dont put anything before God then you are good with God.
It doesnt matter that you love food, but if its place in your heart is above God- sin.
Entertainment above God- sin.
You pursue money more than you pursue God- sin
Etc because all of these things above God are idolatry. You dont have to bow before it and worship it in the traditional way to make it an idol.
If you have no idol be it food, money, lust of flesh, power, entertainment... etc. and instead pursue the Father and His kingdom first.... how would the Father NOT be pleased with your heart having nothing and no one before Him in it?
But if one is convicted to avoid something such as video games... let them listen to their convictions and do not condemn them for doing so.
What is freedom for one may be destruction for another.