If I had to classify this I'd just call it "Freeform". It looks like there really aren't any rules so much as players accumulate trinkets and items and the game master tosses out situations to get a reaction.
You could get some mileage out of standardizing the item formats and handing out "Constrictor" sig banners. They could function as convenient character sheets showing known spells and items. They'd also be a natural way of viral advertising.
If you were going to use actual rules, you might consider starting by adopting an existing rules-lite RPG system. Risus: The Anything RPG is really on the light side, since a character really just consists of three made-up stats (which could be applied to player spells). If you continue with this, I'd suggest trying that as a start and seeing how it plays out. You might modify that system, or make up your own based on those simple dice rolls.http://www222.pair.com/sjohn/risus.htm
Unfortunately, the total lack of rules pretty much limits the quality of Constrictor to the quality of the game master. The players are relying on you to come up with fun situations and amuse them with replies. Players have no way at all to gauge their likelihood of succeeding at a task since they will all be against arbitrary target scores (Like how whatshisname wanted to fart on the character but failed on whim of game master).
If you went forward with this, you would ultimately be responsible for running everything. You're selling the game master instead of the game, if that makes sense.