MS Paint Adventures is not a game. Except that it is a game, absolutely.
The current game in progress is Problem Sleuth, but two previous games have been completed, and are archived. If you check out the first page of Problem Sleuth, you'll see a crudely-drawn private eye standing in his apartment, with the canonical things present you might expect to see if this were a graphic adventure -- a gun, a desk, a phone, a wall safe, a door from the office. Below is a blinking > cursor, which you might reasonably think is an invitation for you to type in text. It isn't.
Instead, below the image is a single HTML link ("Quickly retrieve arms from safe," a bit of a joke, as the private eye in the first image is drawn in such a way that no arms are visible). Actually, occasionally there are branches, but either one dead-ends quickly, or they reunite.
Click on the link, and the image changes -- and a new link is available for your use. With each image is but a single link, which advances the story. The images (and accompanying text) seem to imply that this is a graphic adventure -- your inventory changes, as do aspects of the game world -- but in fact you never have a real choice about what to do next. It's a single, linear story. And therefore, not a game. Yes?
Except that when you come to the end of the story (as it exists so far), you can suggest to the creator, Andrew Hussie, what action the character should take next. Hussie selects one of the suggestions, draws the next image, and posts it, along with a link for that action. Or to put it another way, it's a form of collaborative story-telling with the external indicia of an adventure game, and it is, in a sense, a game itself -- at least to the degree, say, that The New Yorker's cartoon caption contest is a game. If nothing else, you're competing for the egoboo of having your suggestion selected by Hussie as the cleverest (or perhaps easiest to draw -- not sure really what his criteria are, but based on the story, "cleverest," or perhaps "most deranged" sounds about right). It's not actually an "unbranching story;" instead, it's more like a sort of tabletop roleplaying game, with a bunch of players shouting out what the single PC should do next, and the GM deciding which idea to adopt.
Which sounds like a game to me.
Problem Sleuth has the basic issue that any "round-robin" form of story-telling has; logic and narrative coherence are not strong points. Yet it's entertaining in a way, and I imagine Hussie, at any event, is having a blast. And from our perspective, it's interesting in how it uses the tropes of IF in something that really isn't IF at all, but something odder.