I think everyone would agree that a 1 second chess game is silly. How about 2? 3? 7?
Oh you draw the line at 60 seconds? What about 59?
Dionysus, unless you agree with me that 1 second chess games are not silly, your point is "falsified" because it is guesswork.
I never drew the line at anywhere - in fact 10+1 is perfectly acceptable. But your question does raise an important question, which is when does even bullet chess become absurd? Of course at 1 second (without increment) you cannot mechanically play out a game
I think the threshold should be when you can no longer mechanically play a game consistently to its chess-based conclusion (draw, mate, resignation). Then the balance is tipped away from chess towards being a purely mechanical exercise.
For the sprinting analogy, there are many different lengths substantially less than 100m that have meaning and are thus "reasonable" distances (e.g. http://en.wikipedia.org/wiki/40-yard_dash or http://en.wikipedia.org/wiki/60_metres ). The question is at what distance would this no longer be running? At 5 meters this would likely take one leap, so would more likely be leaping or long jump and you would also need to work out whether they were walking and not running (http://en.wikipedia.org/wiki/Racewalking - "it is different from running in that one foot must appear to be in contact with the ground at all times") so the movement of both legs would at least need to be seen once each, and likely twice (since one would be a step, two would be the plural needed for "running"). So maybe 10 meters becomes a mechanical threshold for where something could be said to be running and not walking or leaping? (Yes, just guessing!)
So for chess:
How many moves can something be called a game? One idea is 30 moves (http://en.wikipedia.org/wiki/Rules_of_chess "no drawing or resigning during the first 30 moves")
How long does it take someone mechanically to make a move? (without premove, because I can agree that premove is in no sense classical chess) I would say 1 second is reasonable, although in my experience .5 seconds from opponent move arrival to making your move is quite doable.
Which leaves us somewhere around 30 seconds for a game without increment or premove that reasonably can be played to conclusion in any chess sense.
But, of course, this opens us to the debate of both how many moves should be made before it can reasonably said to be long enough? (29? 28? etc) Or how short a time should be given to allow for a response? (0.9 seconds?) But I am fine with debating those numbers in a purely hypothetical way (since practically no chess server has users playing at these time controls)... but I don't get why there would be any debate at all about 60 seconds, since you are still playing chess, and can finish a game to its chess conclusion.
The overall point is that you are exactly right - if I came up with a number (which I have not, the above is just thinking aloud, not a rule like Atos and others have provided) - you could say it is guess-work! Which is why I will not come up with a number and which is why I say anyone who does come up with a lower-limit is just guessing....
On a side note, maybe someone should start a thread on the very subject you introduced "To bullet players, at what time control is even bullet no longer chess?" - could lead to even more extended and heated debate :)
Hm, you are just pushing the ball back over into my court. I was making a general point that a reasonable (yes I made a typo which you brought attention to, as could be expected) amount of time is needed, finding it is somewhat more difficult but that doesn't falsify the general point. I think that possibly 15 minutes per side might be the minimum for a reasonable chess game, and there is a maximum somewhere consisting of how long the players could spend without being significantly affected by physical demands for sleep, eating etc.
Your position is not simply not logically sustainable. If 15 minutes "might be the minimum for a reasonable chess game" then you are saying 14 minutes and 59 seconds is immediately classified as unreasonable? This seems "silly" :)
And then if you accept 14:59 is also reasonable, then what about 14:45... etc etc etc
Your point is "falsified" because it is guess-work - a GM may find it perfectly reasonable to play for 5 minutes against most of us playing with hours (and still win in nearly all cases). Reasonable is purely subjective.
By "reasonable amount of time" here is meant the time control that enables one to play close to their optimal level of chess ability, whatever that level is, while also not wasting time unproductively. That a GM could beat an amateur while playing way below their standard level of ability is a red herring and has nothing to do with this. Also, "reasonable" is not meant here in other possible senses of "reasonable"; eg I find it more convenient to play blitz than long games on the Internet for practical reasons etc but not for chess-related reasons. Perhaps we could use "optimal" instead of "reasonable" if that will help.