I didn't understand it
I wasn't able to follow what you were going for in the video. I got, sort of, that it was supposed to be a parody though.
I though the music choice wasn't too bad though, kinda reminded me of something like an anime cartoon intro or something.
I might have called it more along the lines of Eddsworld vs Heavy Weapons Guy (I can't remember his name exactly, it's been some time since I've played that game, yeah I know, excuses) because, correct me if I'm wrong, he was the only TF2 character I saw in there.
I didn't think the animation wasn't awful, could improve though, but hey, everyone's could (especially mine, I've tried to animate and it was horrendous). I wish I could offer better advice on that, but like I said, I'm no animator. Practice is what I hear does magic. Art wise, you do remain true to the Eddsworld characters, but it did take me a little while to recognize Heavy Weapons Guy.
It was neither awful nor was it great, somewhere in the middle.