The first online meal reservation system that was used by a large number of people was probably at Disneyworld, and it was the one you used after you entered Epcot. I never used that one. My first encounter with ADRs was via the phone line and then later their website (I'm fairly certain you could set up an ADR through the MyDisneyExperience app, but I don't think I ever have. Altho some of these details just fall right out of my brain). But Disney IT has historically been an inhouse thing they develop for themselves and they never share it with outsiders (which, come to think of it, means there's a future profit center there, should they decide to change their approach).
Currently, OpenTable and SeatMe seem dominant, altho I learned about Rezku when I got an email reminder from them. I'd booked a reservation at Red Raven's website and wasn't at all sure who was providing the underlying service.
Here's an article about Rezku:
Cloud and browser, pretty much exclusively.
Here's a description of how OpenTable works from about 5 years ago.
No wonder it is only comparatively expensive restaurants using this system! Ripe for disintermediation, imo.
SeatMe thinks they can do it, too.
For all I know, there are a dozen more competitors out there. I only started making reservations again very recently, when we got a new sitter who really likes working evenings and who the kids adore. It's been fantastic, especially since a whole lot of great restaurants have opened up in our and neighboring towns. There's still a lot of utility to picking up the phone -- a bunch of restaurants that have had issues with online reservations systems have blocked out their busiest hours for phone reservations only. It'll be interesting to see where this all goes in the next decade.