The dreamcast failure was all due to Sega and no one else

I would say Nintendo kind of helped start their decline (though the big N also did themselves no favors in the early 90s), and even slightly lost their lead against Sega in the US until the release of Donky Kong Country kinda sealed the deal for the SNES victory over Genesis there. But Sega had the tough task of having to chip away at a dominant market leader at the time and compete with Nintendo's typically high-quality games. Nintendo also seemed to at least indirectly coax them into a sort of hardware arms race and other projects over software, which brought lots of dead weight to Sega and dragged the company down shortly thereafter. 

Like the protagonist in Genji II, against a Giant Enemy Crab, Sony inflicted "Massive Damage" on Sega by essentially outdoing them in their own game of drawing third parties their way, aggressive price points, and an overall "edgy" gaming philosophy. They also had superior hardware and a massive quantity of games. Basically there was virtually no reason to opt for the Saturn over the PSX..

By the time MS came along, Sega was in its final throes I'd say anyway, but the original Xbox was sort of the final nail in the coffin. There simply wasn't room in the industry for four major consoles/competitors at that point, and Sega was muscled out by the other three.

So it's hard to say as all three companies played a role in the decline and demise of Sega, but Sony probably was the most impactful (and ironically Sega shooting themselves in the foot - that probably is a close second). Microsoft simply sealed the deal. The war against Nintendo was an epic one, and it took its toll, but Sega was still riding fairly high by the mid 90s, especially in America, and could have rebounded if the right moves were made. 

Sony and SEGA - damn you :)

Sega of Japan was arguably the worst managed major video game hardware company in the history of the industry. Sega of America was possibly the best managed, at least at that time. Absolutely unforgivably stupid decisions from SoJ are the primary cause of Sega's exit from the console hardware market.

As for competitors, I'd say all three share mostly equal "responsibility" in that they were all doing a better job (MS was already doing a better job than Sega, and hadn't even launched their hardware), leaving no room for a poorly managed company to compete.

Of course the main culprit was SEGA themselves, but since the OP asked for competitors, Sony. Their pricing strategy with PS1/2 was still something the other two weren’t accustomed to, and Sony money whipped a lot of third parties.

But yeah, the mistakes of their past is what ruined SEGA. The DC actually had an incredible library of games, great online play, and cool peripherals but SEGA didn’t have money to continue.

I also don’t agree with people saying that maybe without a third competitor, SEGA could have found a niche and survived. That wasn’t their style. Also look what has happened since they became third party. They still make some good games but the overall quality is nothing like it used to be.

Sega is responsible for Sega's failure, nobody else. Sega CD, 32x, Saturn and Dreamcast shortly after. Too much hardware with too little support. Sega destroyed their reputation, nobody trusted the Dreamcast being support, so people didn't buy it.

Just my honest 2 cents. Part of the problem is Sega's 'glory' days is grossly overrated. Sonic was never as good as Mario. Phantasy Star was nothing compared to Final Fantasy. Sega never had anything that competed with Metroid and Zelda. Sega had arcade games.... but the world has moved on from arcade style games.

I cannot say much to Phantasy Star, but Sonic's World and the level design and sense of speed was actually quite something compared to Mario. Sonic never transitioned well to 3D and even the 2D titles couldn't add much more after the first, but that first one was good.

Bold: I would argue that the first 4 mainline PS are on par or even better than the first 4 FF. PS2 is also the first JRPG which has the main heroine died in the story way before the final battle.

I thought Phantasy Star IV was excellent, right up there with FF.  But PS III was awful.  Meanwhile, on the SNES, there was the likes of 4, 6, Trigger, etc.