The Forge definition is faulty and/or useful only in a specific play paradigm, i.e., shared improv and issues of power over the narrative.
For my purposes, it's much more useful to look at resolution systems thus:
1. Does the player have any doubt as to what will happen? That is, is there risk from the player's perspective?
2. If so, then is the thing-in-doubt resolved by mechanics, or by GM judgment? (There may be some fuzzy areas that include both, but let's consider them as separate ingredients.)
3. If mechanics, we can subdivide as we like. The most important categories, I think, are:
a) Stochastic--a straight diceroll or cardflip for example. Rock Scissors Paper is basically indistinguishable.
b) Deterministic with hidden information. I have Strength 10 and I decide to try to hold the door shut against the creature on the other side. I don't know how strong the creature is, but this has been determined in advance. If its Strength is greater than mine, it will force the door open, otherwise not.
c) Competitive resource expenditure with hidden information. This is basically a form of sealed bid auction. Card play in Castle Falkenstein has some of this characteristic, but I don't have the game anymore to say for sure. And I don't think it actually looked like it would work very well.
d) Mixed or subgame. While any series of resolutions could be seen as a subgame (e.g., a melee in D&D), this category applies most clearly to cases where the subgame steps leading to final resolution are strongly formalized; at the extreme, this would take us to the point of being impossible to interpret as "representing" something in the fiction. E.g., Dogs in the Vineyard, extended conflicts in Burning Wheel, The Shadow of Yesterday, Hero Wars, Heroquest 1e.
For each of a-c it may be helpful to show what they look like WITHOUT risk.
a) This is where the PC simply does something and there's no question whether it can be done.
b) This is where the PC might or might not be able to do something, but is informed somehow before trying it that yes, it can be done, or no, it can't. E.g., the player knows the strength of the creature on the other side of the door. Or the player is informed beforehand by the GM that a knife held to his character's throat will absolutely kill him if he struggles.
c) The player is told that holding the door shut will work if and only if he spends a token.
For (d), obviously we'd be talking about some combination of a-c, but in practice I suspect it would either be so trivial as to default to one of them, or so complex that it would resemble Go, Chess, or Checkers. In the latter case, doubt would be reintroduced by the fact that none of these games has been "solved".