I don't think this formulation is precise enough to establish parameters for classic D&D-style "skilled play".The way skills work on 5e is purposely loose so they can take a back seat and work just as an emergency tool for the DM to adjucate actions when he's uncertain of the outcome.
We need to also identify what counts as a permissible action declaration - I poke the door with my pole, relying on my knowledge of doors and poles to put maximum stress on the door's hinges while minimising the tension in my pole sounds to me like it could be (and a Dungeoneering skill check might determine if the PC can actually do what the player wants to do, and have a chance of forcing the door or triggering some other interesting feature the player suspects is there rather than just snapping the pole).
Whereas I use my knowledge of dungeons and their architecture to travel to the 9th level where I believe the prisoners to be chained up clearly is not permissible in any sort of "skilled play" game. But obviously may be a perfectly legitimate action declaration in many other RPGs, including some approaches to D&D (eg action declarations not too different from that were components of the skill challenge I used to resolve the PCs invasion of Torog's lair; and of various skill challenges I used to resolve overland travel).
I think that most RPGs that aren't 3E D&D or 3E-derived will under your example, and hence - if it really is exemplary - will satisfy your definition. So I think your definition might be overinclusive.a take on "skilled play" (modern and original) that may span contexts is to use it as a label for play that while emphasising skill inclusively, is also interested in skill outside the game system.
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a group who aims to perform "skilled play" (quotes) is going to desire challenges that can't be solved (or can't be solved most efficiently and powerfully) using only the game mechanics.
A simple and incomplete example might be that they would look for players to tell them something about how they approach "persuading the Queen by rolling against Charisma (Persuasion)" that makes them believe she will set aside her trait of "will not listen to persuasive words." The group can't just make the check, they must describe an approach to overcoming an obstacle that has no representation in the game mechanics.
For instance, Burning Wheel requires any action declaration to include both a task (what is the PC doing?) and an intent (what to the PC, and the player, hope to achieve by way of that task?). An intent - we want to persuade the Queen - without a task ("I say such-and-such" or maybe "I say words to the effect of such-and-such") is an incomplete declaration.
There is a recurrent problem in RPG design of rules stipulating this sort of thing but not giving it teeth. BW uses two techniques to give the intent-and-task requirement teeth. One is that it has quite an intricate skill system, and until the task is described we can't tell what skill actually has to be tested. The other is that consequence narration for failure must focus primarily on the failure of intent, and so until the intent is known the GM can't let the dice be rolled because s/he can't form a conception of what failure would look like.
But I don't think any of the above supports a conclusion that BW is a skilled play game.
Other games where basically the same analysis could be given, and the same failure to support the conclusion would hold, include Prince Valiant and 4e D&D when a skill challenge is being resolved, Apocalypse World doesn't use intent in quite the same way but also needs task and at least some elements of intent to be specified before action resolution can take place.