Let's ignore the girlfriend for a minute and focus on you OP.
You stand to gain nothing from telling the girlfriend. Maybe a part of you feels that if you told her you would doing a good deed and you would feel better for the shitty thing you did. But you won't (or you shouldn't).
By your own admission you behaved terribly, feel bad about it etc, etc. telling this woman, and doing what you see as a good deed, will not negate what you did, or absolve you from some of the responsibility. I think deep down, you're hoping it will. Or hoping it will ease your guilt somewhat, but it won't.
The best thing you can do, for yourself never mind anyone else at the moment, is walk away. Their relationship was never yours to get involved in, by telling the girlfriend you are once again putting yourself in the middle of their relationship and no matter what the motive is behind it that is wrong.
I know you'll say "but wouldn't you like to know?" and yes, personally if my DP was cheating I would like to know, but I wouldn't want to find out from the OW, and it's really not your place.
Not only that, you say he's just going to do it again etc, but you obviously don't know him very well as he's lied the whole times he's known you. From what you've said I don't think this is the case but what if him and his girlfriend are very happy, he's realised what he did was a mistake and won't cheat again? What if from now on they can have a very happy relationship with no cheating? What if they potentially have a really bright future ahead of them where they're both happy, so is their son, they have more kids, get married and live 'happily ever after' and he looks back on his three months of infidelity with shame? I'm not saying all that will happen, but you're trying to justify telling the girlfriend on the basis that she'll be really unhappy when you just don't know. You may have an idea but you still can't be sure.
And the videos need to go. I'm not sure why you've kept them. If you do plan on telling her (after all the advice saying not to) then if she doesn't believe you then why trot some videos out? They'll do more damage than good. If she doesn't want to believe you then she won't. You've also said you have a lot of text proof- the videos are not needed to prove a point and you really should delete them.