It's not (quite) the ridiculous pseudoscience that it sound like. Automatic (self-winding, by means of a weight) mechanical (i.e., clockwork) watches run down in a couple of days if not worn. If you have several watches, this means that you have to keep resetting and winding up your watches -- and some don't even have a crown on the side for winding. So there's a market for watch winders which move the watch around to keep it wound up.

The thing about gravity comes from trying to make mechanical watches as accurate as possible -- they run at slightly different rates depending on which way up they are, so are sometimes calibrated to an individual person's lifestyle (e.g., a computer user spends most of their time with the watch horizontal). One way of overcoming this is the tourbillon which continuously rotates the watch's timing mechanism to even out the variations in the watch's position. It seems that this product lets the watch rest in different positions after each winding rotation in order to have a similar effect, and hopefully maintain some semblance of accuracy.

And this is why we all wear quartz watches :-)

Are you aware of http://www.roombaexchange.com/ ? They do repairs and spare parts, and also sell second hand bits of dead Roombas, so if you want to abandon one, at least it will go to a good home!