So earlier today there was a tweet
an app called airDnD where traveling nerds can find a role playing group to join for a night— Rebecca Watson (@rebeccawatson) November 7, 2017
What you're going to get here is how I'd do it. Some of this is stuff you should just do, and others will be "I think this sounds good, but investigate please". Basically, if you want to do this, take this and run with it. If you can make it work, some credit (or large piles of cash) would be appreciated.
So, first up: the name. Change it. Pick something, pick anything else, or Wizards of the Coast and AirBnB's lawyers will play rock-paper-scissors to decide who gets first crack at taking everything you own. The name as an actual used name is toxic, but it's great for explaining the idea to people.
Let's start with the supply side: GMs. Why would someone GM for you? Well, same reasons as AirBnB and letting people into your home: money. The GM process goes as follows: they specify a date, a system, a brief plot idea (e.g. AD&D, "Classic Tomb of Horrors, no prisoners taken") and a few other details I'll go into later (food, player slots, etc). Basic idea is this is like a convention time slot: so typically 4 hours, with everything happening during that. They also say how much this is going to cost. Because I'm not a complete asshole, minimum money to the GM is based off the Real Living Wage, assuming also 2 hours of pre-game prep. They can possibly scrimp on the prep, but their ratings will drop, so up to them.
Other things the GMs need to provide: location. Preferably their place, or somewhere else non-grotty. Again, this is basically up to them, but I'll talk about the intro process for GMs later on. Food in some form is also expected - this either comes down to snacks or takeaway (possibly an option for GM-prepped food for a premium, but that gets fiddly legally speaking). If it's snacks, part of the costs are a snack budget (canny GMs running many games may be able to reuse stuff, but the budget stays still the same); takeaway is assumed to be each person chips in reasonable numbers, but that's external to the platform. Expectations from GMs about this sort of thing should be either in their profiles or discussed with players beforehand.
So, costs in total are: GM time, possible snacks budget (money goes to GM), and some cost of the platform. Divide that by the minimum player count, and that's the advertised cost. If the player count goes up, the per-player cost drops, but players signing up are agreeing to the minimum player count cost.
Why would I trust a new GM? Or their new location? Well, each have to be vetted. AirDnD would have a set of veteran roleplayers who will test new GMs in a system and new locations. New GMs, existing GMs wanting to do a new system, or new locations will only turn up on the internal systems until they've gone through vetting. Games on those are paid for as per regular ones, but if they go well (for values of "it went as we might expect for this system, the GM appeared competent in running that system, and the location didn't suck"), then the GM is marked as allowed for that system, and the location is now usable.
Ok, demand side: players. You find a game and you sign up. If it's something like D&D and you need specific types of character class (which isn't for example the case for say Paranoia), you pick one or more of the listed available classes. There's a little bit of per-game stuff here, but not much. At that point you agree to the cost (which is the maximum for that game given minimum player count), but aren't immediately charged. If a game you're signed up for reaches it's minimum player count (and in the case of character class games can find a mix of players that don't clash in class requirements), you're immediately added and charged. You can sign up for multiple games in one evening, but if one of your games gets full enough, the others are immediately dropped (Assumption: only one game per day. This doesn't support weekends of gaming well). You can also manually remove yourself from any game that hasn't reached minimum count yet (bonus points: allow players to swap out their places in games with at least their minimum count with another person). You can also add yourself to games that have their minimum count, but haven't reached maximum yet.
There's also all the usual stuff - profiles, comments, ratings, chat between the people involved in a game once it's got enough folks. There's also a bunch of extra details: start times, "we'll start even if you've not arrived" times, etc, etc, but that's getting into the weeds now and I think you've got enough to be getting on with. I'm slightly worried about what this would do the currently free pools of convention GMs, but I think this would result in more good GMs in the world, so I'm kinda cautiously optimistic about the overall idea.