Warning: this post contains minor spoilers for VESPER.5 (though nothing not clear after a week or two), and also asks whether certain things are games or not. Note that I do not consider "not a game" to be a value judgement, and I'm interested in finding edge-cases and exceptions to made-up rules because such things are often more beautiful to me than that which is easily classified.
Game idea: You walk around in an empty room and nothing happens.
Is this even a game? I know some who would argue that it is, and some who would argue that it isn't. If it's a game, it's a fairly trivial one. There is a decision to make - where to walk within the room - but it has no further consequences. Still, the first time you play you don't know that nothing will happen, so there is some ambiguity.
Game idea: You walk around in a room with paintings hanging on the wall; if you move next to a painting you can look at it.
Okay, now we've ramped up the consequences a little bit. You can choose what to look at, and see a different image depending on your choice. It's purely an aesthetic consequence, it's not a complex system of interactions, but that's okay. Uncertainty arises from not knowing what the pictures are until you look at them. Is it a game yet?
Game idea: You walk around in a vacuum-filled room with paintings on the wall, wearing a space-suit with only enough air to take 10 steps.
Now the consequences have been turned right up: you don't have enough steps to look at every picture, so there's a resource constraint giving exclusive alternatives. You make choices with opportunity costs and uncertain outcomes. I'd say it's definitely a game - though a quite simple one and probably still an edge case for some. (Further evidence in favour of it being a game: it's in SPACE!)
Game idea: You walk around a room looking at paintings, but you can only take one step each day.
So we've arrived at something a bit like VESPER.5. There's no exclusivity; if you invest enough time you can see everything; but decisions still carry real weight because they cost you in real time. It definitely feels like a game.
Game idea: You walk around a room looking at paintings, but you can only take one step each second.
Is this significantly different from the previous? Your choices carry less weight because they cost less time, but they still do have a cost. Time is a finite resource for mortal beings. You can continuously interpolate from this to the previous game just by changing the time parameter. This is an obstacle to having a strict definition of "game" that excludes one but not the other - ideally we'd like our theoretical analysis not to depend on time scales, not to switch at some arbitrary parametric value.
Proteus is not very distant from some of these examples. You spend time playing it, making choices with outcomes that are largely experiential - what scenes you're looking at, what music you're listening to. It has deeper mechanics, complex interacting systems of cause and effect, but still they're aimed at an aesthetic effect rather than classical gameplay. It's a piece of entertainment software in which you make decisions about allocating resources (time) with uncertain consequences; a game. (Though that description feels somewhat absurd - while true, it fails to describe the heart of Proteus.)
I realised this playing SpaceChem, which would typically be classified as a puzzle, not a game (in taxonomies that distinguish puzzles from games). At a formal level, there are no truly uncertain decisions made - you can try out any possible solution and then undo the construction with (seemingly) no cost. But the cost of time means that's not the case, and you can't reasonably try all the possible solutions. You have to plan how best to spend your limited time to search for a solution. Laying out a complex chain of reactors can take half an hour or more, and once you've committed that to building something you'd prefer to adapt it if possible rather than clear it and start from scratch. As in a game of Tetris, you deal with the consequences of your suboptimal placements. The same is true of any puzzle; even if there's an undo button, you're still expending some of your finite lifespan on false attempts.
So player time as a cost means things that we naturally think of as being "free"; reversible choices with no in-game resource cost; actually aren't. Taking a step in VESPER.5 feels consequential, and it wouldn't if you could just step right back the next moment, but that's not a fundamental difference - we've just turned up a knob, zoomed in on a choice that would be there anyway.
In Meier's "a game is a series of interesting choices", what makes a choice interesting? The classical answer is that a choice is interesting by being difficult to make, because of some form of hidden information - whether explicit (as in Poker) or implicit (as in Chess). But there are other ways a choice can be difficult or interesting. If we abandon the notion of a single unified objective, the choice of what goals to pursue can be difficult and interesting because the outcomes are incomparable. This is a closer approximation to real life: we pursue varied goals with varied - sometimes contradictory - objectives; not everything has an economic value, a moral value, an aesthetic value; sometimes these values fight each other. In VESPER.5, you ask yourself it's worth your time to stop and smell the flowers, or if you'd prefer to race deeper in as fast as possible, or perhaps ascetically skirt the edges while avoiding touching anything. There's a "hidden information" aspect to this too - you don't know if the program will react in different ways to these different inputs - but more interesting is the unique personal valuation.
James Lantz wrote recently about player time in games - he said a bunch of stuff that I'd been going to say in this post and some smart things I hadn't thought of, so read that.