If I play chess, and someone changes the rules so pawns can now move in any direction, and rooks can now move diagonally, and kings can now move any number of squares, am I still playing chess?
That said, if you say to the person you are playing against, "But those are just optional rules. You don't HAVE to play it that way. I am, but you don't have to. It's up to you if you want to challenge yourself that way or not."
Do you think the other player is going to not use the new rules when the entire game is now designed around the new rules?
Comparing chess to dnd is apples and oranges. Chess has a set of rules where you HAVE to play that way or else you can't play the game. In DnD the rules are there as a guide. If not a guide and you HAVE to play 5e the way it is, then homebrew rules would not exist.
It is not that far-fetched. There are flavours that you can change freely - chess should not be black/white, you can use other colours (this is what Dms change in DnD). It will not change the game. But if you are changing the fundamental rules, you have another game.
There are core mechanics in DnD that no DM will ever change. Rest system and action economy are at the very heart of the system. You change one thing - the whole system falls apart. Food eliminates healing and rest, breaks the rule of Bonus Action, makes some spells useless, changes encounter levels.
With that addition, you literally bring checker's rules into the chess game. Systems are incompatible - it's either DOS or DnD, together they do not work. Once again, Larian did not say "we are using our homebrew variation of DnD", no. What was promised is 5e, and 5e people expect.
