Maybe it was a rat, which legged it past the tumbler at great speed, whacking it hard but really low down so it didn’t overbalance.
BTW, the surface wasn’t like sandpaper - I can’t remember the name of the material. It was that of textured hardened plastic laminate that goes on the top of chipboard kitchen worktops.
Melamine or Formica or something probably.
Is there any possibility that the starting position of the glass might have been not quite where you percieved it to be, but next to something (I don’t know, maybe a chopping board or similar) that fell over and imparted a glancing blow to the side of the glass?
JJ, if I understand your OP correctly, you observed some unusual phenomenon, one that you concede could have one of several (possibly unlikely) non-paranormal explanations, but in your mind you also tag on something like “but it might also be a paranormal phenomenon”.
Then you ask is there any top-down theory that might allow such paranormal phenomenon.
I would say “NO”. In fact it is this absence that makes the “possible” non-paranormal explanations plausible (they do have supporting theories), and the “possible” paranormal explantions implausible.
The capacity for us to generate “possible” paranormal explanations (PK, Poltergeists, Glasses have souls, evil-kitchen-pixies, etc.) ad nauseum should reductio ad absurdum lead us to question our (innate?) desire to have every event wholly explained, or admit of some paranormal explanation.
Melamine, that’s it.
TGU, you have summarised my OP rather better than I did. Thanks.
You are also probably correct, though as a counter-argument, I should point out that one could apply reductio ad absurdam to the many explanations for events that our ancestors took to be “paranormal” (the sun, seasons, thunder, etc.), yet if we were able to give our physical explanation to them at the time, it would have seemed no less fanciful than their contemporary occult explanations. However, since this argument could be applied to any strange belief, it is probably non-applicable as a basis for theorizing.
Hey, sometimes the real explination IS pretty wierd and amazing. Personally I find it infinately more amazing and awe inspiring that a glass could move across a counter without a ghost or other supernatural entity involved. Throwing in gods and monsters in the mix just gives it a simplistic feel to it that seems to go against the complex nature of reality. (all IMO of course)
It could have been a tiny quark mouse that upset the atomic structure of the cabinet surface giving it an unsual viscosity… 
Epimetheus, just so we’re sure, I’m not “throwing in gods or monsters” - I make that clear in paragraph 2 of the OP.
Now, what about thousands of Nanomice singing “we will lift it”?
I know, was merely making a figure of speech. Nanomice it is. LOL.
I think this is a very salient point, modern reductionist explanations rely on a great wealth of knowledge and shared understanding that simply were not unthinkable previously. It inclines us to ask the (unanswerable?) question “Would human understanding of the future be correspondingly indigestible to us?”
I think that the answer is no – we have “grown up”. Having made one mental leap, then to believe that there are more to be made would not phase us. We have a weaker attachment to our “beliefs” than our ancestors. We know how to say “Show me the money!”, we know what it looks like when we see it.
Of course, I say “we” – if only I could mean that universally! Some people have such a poverty of understanding and appropriate vocabulary that it would be uncharitable to blame them for the clumsy “world-views” that they inevitably adopt.
That’s another topic.
As a PS: I agree with Epimetheus that this world is abundant with richness which is dulled by the uncritical descriptive models of the paranormalist.
1.) I once saw a magician apparently levitating a spinning disc. I was up close and watching carefully (there were only three of us in the room, which was very well-lit). I did not see how it was done. I strongly suspect fine thread, although I didn’t see it – and I know enough to look in unexpected places for the string. It almost certainly wasn’t done with magnets, either. I’ve got a Ph.D. in physics, and I don’t know how it was done. And this was an acknowledged “magic” trick – no paranormal activity involved. Moral – a well-done bit of close-up magic can be devastatingly effective and undetectable.
2.) IIRC, I read Randi describing a similar effect to what you saw – Russian “psychics” have been moving glasses around on table tops without any apparent touching for decades now. See Randi’s stuff for further details.
3.) Joseph Banks Rhine did a lot of work at Duke on measuring what he felt were PK effects. He came up with a series of properties and rules. The problem was that no one not in the PK community believed the rules, because they didn’t believe that the existence of PK had even been properly demonstrated. They still don’t. That’s why tests center on proving the existence of an effect, rather tha trying to explain it. See Martin Gardner’s book Fads and Fallacies in the Name of Science, or C.E.M. Hansel’s book on psi phenomena.
Dash it all!
For "not unthinkable " read either “not thinkable” or “unthinkable”.
Don’t you just not dislike no double-negatives!
The late dr. Rhine believed in parapsychology, but he died a broken man. His heir-apparent (I forget his name) was found to have fudged a lot of experimental data, and retired in disgrace. Last I heard, DUKE UNIVERSITY no longer supports the parapsychology laboratory. There are a few holdouts, among them a man named Dean Radin (formerly of UNLA). Radin claims that PK exists, although he has no theory as to the mechanism ofhow it operates.
My conclusion:if there were anything at all to PK, someone would have proved it by now-there has been well over 150 years of research in this area. Even the great Michael Faraday investigated PK, and concluded that it did not exist. My theory is: a belief in PK is a wish upon the part of the believer-they cannot accept that the universe is so indifferent to the fate of human beings. The idea that humans have some measure of control (via the mind) is an idea that many humans find enormously comforting. I take the skepticalpoint of view-like the man from Missouri says: “show me”!
When James Randi was in Dallas a month or so ago, I had the opportunity to go to desert and coffee/wine with him after his speaking engagement. (Jealous anyone?)
I got to spend about an hour to an hour and a half sitting right at the table discussing stuff with him (Along with a handful of other people).
Occasionally, to illustrate a point in one of his stories we would do a minor trick here or there with stuff that was just lying around on the table.
This was a situation where about a dozen people were within feet or even inches of him (as well as people looking over his shoulder) and we could not spot how he did most of the little stunts. Nothing paranormal going on at all, but damn… some of it was mind-boggling.
Randi may be getting older and “not practicing” any more, but his hands are still a lot faster than any pair of eyes at that table on that night.
We will lift it, we will shift it
We will mystify jjimm, jjimm, jjimm
We can move it, we will prove it
We will terrify him, him him.
Mangetout 
Dean Radin is the present darling of the parapsych set, and his book was touted as being a major breakthrough. But his interpetations of data and use of other people’s data is rather fudged. See an evening with Dean Radin for a examples of how he is finding correlation wherever it pleases him.
Just in case anyone is wondering what the hell that little poem was, I was alluding (as was jjimm, I believe) to the mice from the Marvelous Mechanical Mouse Organ in a children’s TV programme called Bagpuss; the 25 second WAV on this page should explain everything… well, maybe.