If Nintendo vanished tomorrow, the industry as a whole would be fine. Whatever void they left would be filled in time. The landscape of the industry would be changed, but the results would be the same.
But I would have almost no games to play. I probably wouldn't own a game console. The amount of money I spent on video games every year would drop from several hundred dollars to...well, maybe zero. Maybe simply less than $100. The amount of hours I spent playing video games every year would drop from about a thousand to fewer than 100. Not out of spite, mind you, but lack of interest. So, for me, Nintendo is THAT important.
In the grand scheme of things, Nintendo is important. Currently. On the hardware side, they command 85% of the handheld market. On the software side, they are one of the biggest publishers in the industry. If they vanished, they WOULD leave a mighty big void. And if, instead of simply vanishing, they were to cease hardware production and become a third-party? Well, their hardware would be missed, but most notably, they would probably be the biggest third-party in the industry. I think you'd have a hard time arguing then that they "aren't that important."