Dislike it all you like. According to AndyK, who runs the Story-Games forum that was what people were objecting to in My Life With Master that meant that it couldn't possibly be an RPG - so they came up with the term "Story-game" to describe it. And it's the main point of difference between a lot of story games and most trad RPGs.
Sense when has an appeal to authority ever carried any weight with me? If that was sufficient, citing that Wick was a game designer would be enough to get me to agree with him. AndyK is simply wrong. He's wrong at the level that we can point to counter examples. Hillfolk is pretty obviously a story game, but is open ended. If we play Tomb of Horrors as a one shot, and that tournament style format is my tables sole experience with D&D - every time we play it we run a stand alone scenario - then by AndyK's definition D&D is a story game. Worse, we've now covered a set of games with goals and experiences that are radically different. If by story game we are accepting D&D at its most tactical and least story centered mode of play belongs to the same genera of as a narrative generation system like Hillfolk, then surely the central element that they share is not a focus on 'Story'. The term we've chosen 'story' is far less descriptive of the group as a whole than something like 'short' or 'closed'. It would be like defining story as the characteristic that distinguishes short stories and novels.
The more examples I think about, the more I'm certain that the difference between a story game and an RPG is a lack of procedural mechanics. If you look at a traditional theater game (and working with the assumption that those games belong to a different class of games than D&D), you have a director that will assign roles and motivations and dramatic goals at the beginning of a scene - and sometimes intervening and prompting players if the scene appears to be flat. Theater games have no procedural mechanics. By and large story games play out exactly like theater games with one major exception - they have some sort of fortune mechanic that at least in part replaces or informs the role of the director in the game. So by referring to those mechanics, you can decide what the roles are like, what sort of elements the scene might have, what sort of motivations the characters might have, and how the scene is to play out - as tragedy or comedy, or which character is intended to get the upper hand in the scene. But in contrast to RPGs, story games like a means of resolving the actual process of the scene. They rely on the players sense of timing and drama for how the processes are to play out, bearing in mind the stage direction given to them by the narrative or director mechanics. "I got the low dice, I have to figure out how this goes badly for me." Where as RPGs use fortune mechanics to resolve processes for individual events, story games are focused on resolving processes at the level of scenes.
Consider a game like Dogs in the Vineyard. This is clearly a nar game with a focus on creating story. But the game still allows for process resolution within the scene - whether or not you intimidate or persuade, whether or not you can beat a character on the draw, etc. Dogs in the Vineyard remains an RPG with a story focus. My Life with Master moves one step further away from that. It's a story game with a clear RPG heritage.
I'd not go for that side at all. "In an RPG you can and are expected to use pre-existing elements of the fiction for which there are no clearly defined mechanics in the rulebook." To me that's the critical difference between an RPG and various games like Descent and Arkham Horror.
It is certainly important, and I'd like to go there. But if I went there, I'd be as bad as Wick. I admit that 99% of RPGs as they are played at tables assume that the rules set is open ended - that is they assume the traditional "Rule Zero". But just as 99% of RPGs as I've seen them played at tables involve some amount of method acting, I don't agree that any RPG that is played without method acting isn't an RPG - because tables can still choose to play them without method acting and they'd be missing IMO but still playing an RPG. This is obvious to me as a computer programmer where I know Rule Zero can't be implemented - yet Mass Effect is surely an RPG - but also because I know some tables hate Rule Zero and do play with a largely closed set of rules were nothing that isn't explicitly permitted is allowed. Yet, just because there imaginary space has a one to one correspondence with a game board, doesn't make it less of an RPG. Consider my example of Chess played as an RPG a simplification of the type. There'd be rooms in the dungeon. There'd be roles to play in the party. There'd be monsters to overcome and goals of scenarios. It's an RPG.
Which bit of "Whose line is it anyway"?
Well, all of it.
Tabletop RPG or Trad RPG. Or even Tactical RPG.
It still think it's not reasonable to relegate D&D to being something other than an RPG. Saying that D&D is a TRPG is in the same category of saying its "not an RPG" if by that you mean it belongs to a subcategory of this sort, and not merely "an RPG played on a tabletop". Plus, story games are played on table tops as well. That's as bad as saying that "story game" is meant to exclude types of play based on length.
No argument. I'd also call it an RPG.
Why? It is a theater game with some randomization elements regarding the roles and scenes you play.
The objectives of the subgames in Whose Line is it Anyway are almost entirely meta. Montsegur 1244 has logic following from the characters.
No wait a minute. Theater games also have logic following form the characters. Absolutely the scenes in WLiiA involve following the logic of the stage direction and the assigned characters.
On this we agree

Where we differ is that Story Games
are RPGs
Only if we use RPG as the umbrella term for all sorts of dramatic play. I don't agree that that is the best approach.
Nope. Doesn't fit either My Life With Master or Monsterhearts (which bills itself as a Story Game). Or about half the other games under the banner of Story Games. Of course what they choose as stats is ... non-traditional.
They have a fortune mechanic, but it doesn't dictate the process of play. Focus some more on that 'non-tradional' aspect.
"Thou shalt not be good at everything."
Trad Drama isn't a game in the same way.
No, but it is play.