for the most part, yes. though it's easy enough to take the name and make the game in the same vein of the original without it being an actual sequel or remake. though in the way of extended universes, if the original developer/studio comes back to the franchise
and makes something to contradict or wipe out something previously done, then that's fine by me, it's their ip to do with as they see fit...as long as they don't overdo it to lucas-esq levels.
When the original developer leaves a series and the new developer take over, do you consider the series to be sequels?
That hasn't stopped some series from being destroyed by the people who inherited it. Take "Star Trek" for example. Berman and Braga turned it into something completely different than Gene Roddenberry's original conception.
Then there are some series that change hands and it all goes well like "HALO 4" for example.
Canon is always regarded as such as long as the source Medium is the same. If one form of Media has a sequel it is Canon as long as it stays in that same Source Media. An example of this would be the Movie Alien to the Movie Aliens,
they are both Canon material and regarded as such.
Not following this rule negates it by default of not being Canon. An example would be, the Movie Aliens and the Video Game Aliens Colonial Marines. It was claimed as a marketing tool that A:CM was "canon" but it is not. Hypothetically to demonstrate a different
Source Media is not Canon would be to say, if a Movie Sequel was released from the Movie Aliens that disregarded any "material" from the Video Game A:CM, it would by nature trump and default the Video Game of A:CM not being Canon.
It does not depend on "who" creates any Medium but solely if that Medium is the same as the Source Media.
If the developers say its canon then their is nothing you can really do about it but accept it. Of course there can be multiple "Canons" in a franchise like Mario for example (Mario RPGs, Paper Mario, and Mario Platformers are all separate canons)