Yes, this is as sure as Apple will not be the only smartwatch maker to achieve success in the marketplace, just like they aren't the only smartphone maker.Many current makers will not adapt and many of those will fail because of it (this will happen- I'm looking at you BlackBerry), but you're right that others will most certainly change with the times. They are smart enough and have to.
Watch companies went out of business and merged with each other during the 70s quartz revolution. And you are right, some of these watch companies are not just smart, but they are innovative, and have even higher quality standards than Apple. They will make formidable competitors if they get the software right. Heck they don't even have to develop their own OS, just integrate it with Apple's and whomever else's.
In the end, I'm not convinced that everything will go the way of the smart watch. Semi-smart watches with programable chips, and/or sensors embedded in traditional watches, may be enough for most, or make great alternates for days when a full blown smart watch is not required.