The pie analogy doesn't quite work, because it leaves out the issue of player acquisition - something traditionally done by the leading RPG in the industry. D&D is the only mainstream brand the industry has of its own (no matter what the difference in sales between the leading games are), and WotC is in a position to leverage that to grow the industry in ways that other companies can't, although Paizo has made some inroads into that with its Beginner Box and various branding initiatives like comic books, toys, and so on. So a successful D&D means a bigger RPG industry with more players in it.
Plus, of course, actual competition makes people bring their A-Game. Neither company can coast. This benefits everybody!
I think you have to differentiate between the brand and the game. 'Dungeons & Dragons' will probably always be THE thing people think about when they think of role-playing games. But to amateurs, Pathfinder
is D&D. So i
s 13th Age. So are various OSR clones.
If I were to introduce a bunch of new players to the game today, I would run 13th Age. But I would tell them it was D&D. Because it is really close, and explaining the fine distinctions would just confuse them. You roll a d20, you kill monsters, you take their loot. Same idea.
There are many different games that can represent D&D, and not all of them are made by WotC.
Intuitively, I expect the main thing that brings new players into the hobby is other players. Joe invites Jamie to sit in on his weekly tabletop game. She likes it and keeps coming back. Whatever Joe and Jamie play every week is 'D&D', as far as Jamie knows.
Really the hobby is best served by having healthy communities of players, not by a particular company or ruleset.
I think this golden age of indie games we are in means more and more people can find a version of D&D that they can really connect to. Hopefully that will bring in more players. But it may mean that the big guys have to get leaner.
And honestly that would be in line with every other industry in the digital age. The long tail of the internet means people can find AND produce stuff more easily. It makes it harder for the big, established players to stay big. I don't think that TRPGs are immune from that disruption.