When I talked about ignoring Otherworld Comedy it was about that as well, in the era in which there are various arguments about Sonic fans themselves about "Characters not feeling the same" and "Sonic can never be consistent with characters", acknowledging a material that addresses that while paying respect to what came before is just a perfect approach, which is why I love Otherworld Comedy from a character and world settings standpoint (Which is my kind of thing, I write tons of blog posts all about that after all).
When I look at a Crossover, I want all sides to be properly depicted with all their nuances, if you don't do that, you aren't bringing those characters to a common ground, you are bringing a basic visual to engage with another one, without the actual baggage from character and world.
It seems that the episode already had a decided result long before all the recent stuff and all they could do to deal with recent stuff was "We know it happened, but it wouldn't change anything", which I fear is the worst way of approaching any type of content (Not taking into account impossible changes due to deadlines and resources). It can get even worse due to when this video was released, Sonic had a very constant push of content this year about setting right character and world aspects, all of which would not be actually used in the video due to development preparation (For real, as much as it makes for good marketing to make a video around the time of a new release, the fact that the video can be outdated by the time of release really should be something takes into more consideration).
What I think happened is that other than Wiki-level research for mechas and other random stuff to fill scenes with characters, no deeper thought was actually done to represent the characters properly with respect. It really gives way for depicting Browser's side in a certain light, but not doing so for Eggman, especially since the latest development (Again, I have no idea for how long the fight has been worked on and what their initial thought about the character was, so it could very well be the case they had a certain targeted plan for the fight and decided just to follow the plan and adjust new findings to what was already the plan, instead of backing down from the plan to fit the discovered material to it).
In the end Death Battle just is more likely than not to not care about those points, which will forever put them into a placement that doesn't matter personally to be, but due to their size and influence, will definitely shape the understanding of dozens or hundreds of persons, so I can't wait to see people thinking the DB depiction was true to the world/character settings.
To myself, the way of countering it is by making or promoting content that depicts the world and character setting as I think it would be fairer, sadly I don't know if someone is making Sonic content that does that (Other than Windii, but her is more translation so people can get this kind of stuff), so I'll instead just continue working until I release my major Sonic post, a study on the idea of "Unified Sonic", trying to showcase the core thinking of Sonic that existed since the started and could be explored again to both bring forth Iizuka's idea of having one Sonic, while giving the freedom for creators to not be limited by "one world and history", while still giving the character and world proper respect (As you can see from the way I write, I think more about using and respecting as many character and world settings as possible, giving them what I think is "fair depiction". It's one more reason the "let's make a meme" approach DB sometimes uses not feel right to me, as almost always it's done by disrespecting the "defeated character", which I think is not fair, you can have a character be defeated and still give him proper respect. Just look the way DB depicted Infinite to how Otherworld Comedy depicted Infinite, even in "death").