Sony, as the announcement, and specifically the overhyping of the graphical capabilities of the PS2 (which were nowhere near that level they hyped it up to during the reveal) took out all the wind of the Dreamcast's sales, which was doing quite well until that point, even having supply issues back then. By the time people realized that the PS2 wasn't as powerful as it was hyped up to, it was already too late to save Sega as a console manufacturer.
This absolves SEGA of most of its responsibility for its own demise, which is, quite frankly, nonsense. No matter what the "hype" stated, SEGA is the leader of this collapse. Most posters here have nailed it! Mismanagement and being unprepared to take on more fierce competition is what did them in. In other words, they themselves were the biggest reason for their demise, not anecdote of "failed promises" from the PS2.