1. Good for you, but we're not talking about For Glory.
2. Mewtwo's defense is not super strong. It's just better than his offense. Rosalina's defense is strong because of Luma and because of Rosalina's range on her moves (tilts, nair, etc.). Mega Man's defense is strong because of his ability to throw out multiple projectiles quickly that cover various areas around him. Mewtwo's is ok but it's not strong because everything he doesn't deny area control as effectively.
3. I understand the playstyle that you're supposed to implement but linking me to a match against Luigi and Falcon (a good Luigi, but still not relevant) doesn't prove a point nor does it show what to do against Doc. If you just assume that Doc has the same problems as Luigi then I don't know what to say really. Doc has a low shorthop so it's going to be harder for Mewtwo to fend him off when he gets in or to punish him by grabbing. Doc doesn't have traction issues like Luigi does so he can punish you harder. Doc doesn't have bottom 3 airspeed and is not floaty so he cannot be juggled as easily. Having Tornado to blitz through moves and mix up his landing is a huge boon. Luigi cannot do this as well with his Cyclone. Based off of the video you linked and the points above, I'd say Luigi has a harder time than Doc does against Mewtwo. Pretty strange that you have Luigi as an even matchup but Doc as an advantageous one.
Mario has an easier time because he can catch up to Mewtwo and combo him, but as far as KO potential is concerned, his punishes are not nearly as rewarding (this character cannot kill without Up-Smash or rage) and he cannot edgeguard as effectively (Mewtwo has an advantage here). Mario has no reason to use FLUDD against Mewtwo, unless he's in the lead or if the Mewtwo player tries to recover and fails miserably. Even then, FLUDD is not a move that should be used in neutral because it doesn't do anything useful. Fireball is more useful here.
I could also say in a best of 3 setting, Mewtwo loses to Doc because of this.
https://www.youtube.com/watch?v=xpQ3PC4uU6A - And Kudemo is, in my opinion, a pretty good Doc. But I don't think either of them were that familiar with their character's options. Zudenka is more familiar with Yoshi vs Doc because they play that matchup frequently.
4. It's funny that you think Doc is great against characters without projectiles and just wins trades.
5. You keep saying this without saying why. Mewtwo's d tilt is not the answer to everything and Mewtwo does not hopelessly outspace Doc otherwise. Doc's down tilt has pretty decent range, and comes out 1 frame faster. Bair comes out at the same speed as Mewtwo's D-tilt, does more damage and hits characters whether they're ground or not more consistently. Jab has pretty decent range comes out frame 2.
6. Matchup weaknesses which have stemmed from a poor understanding of Doc. It's fine to think a character wins or loses against Mewtwo, but you don't understand the character so your theory does not apply. And linking me to matches of other characters to prove a point is laziness. It's this kind of analysis that makes Doc seem much weaker than he actually is.