Can't say I've noticed this exact behaviour, but I have noticed with the Steam version (I registered my GOG key on the Unepic site to get my free Steam copy) which is 1.43.4 that on my second running of the game the motion was a little stuttery. I minimized to the desktop then maximized back to the game and it was fine again. Don't know if this is related but you could try switching the window to desktop and back to see if it works for you.

No, that didn't work. I'm still getting delay when entering commands. I'm using Win 8, of the 64 variety. Anyone else? It'd at least be comforting to know I'm not the only one. Google isn't turning up much, either.

OK, it's been a few days, and nothing else has come up. I'd really like to play this game that I can tell would be tons of fun if it would work, but I don't think I can if it's not functioning. What's the procedure for GOG refunding a game that doesn't work?

You need to speak to GOG support staff for help with your issue. It wouldn't hurt to speak with the Unepic developer via the official site, too, as Unepic is a game that is still getting new versions so if there is a bug then they might be able to fix it for a future release.

As for refund, I very much doubt you'll get that.

Firstly, the game you download from GOG is DRM free, so you can use it on any number of machines at any time, no activation needed. So once you've downloaded it (as GOG can tell once a game has been downloaded) it is in your possession to do with as you will. If the game had not been downloaded then GOG know you don't have it and can refund it, but this is usually only needed where errors have occurred in the purchasing transaction, such as buying a game instead of buying a gift or cancelling a pre-order. But once you've downloaded a game, you have it.

Secondly, how can you prove to GOG that you have the issue? How can you prove it is the game and not your machine? As said above, you have the game installer and can make as many copies of it as you like, so for you to get a refund you would have to prove that you have deleted all copies that you have. This cannot be done. So there is no refund policy here as from GOG's point of view you could just be looking to get your money back whilst keeping a copy of the game.

You should read the GOG terms of use before you use the site. http://www.gog.com/support/policies/terms_of_use
Here is the refund policy:

Refund Policy

You can cancel a preorder and receive a full refund if you request this before the preordered game's release. The refund request becomes invalid if you attempted to download the game, or its bonus content.

You can request a replacement game of equal or lower value (for games purchased during discounts, the discounted price applies) if the request is made within 7 days after purchase, and you have not attempted to download the game or its bonus content.

A sale is considered final after 7 days after purchase, or when you make a download attempt for a game or its bonus content.

That all makes sense, which is very frustrating; I hate buying unusable games.

I already made a thread on Unepic's site, here:
http://www.unepicgame.com/phpBB3_en/viewtopic.php?f=3&t=1721&p=9689#p9689

No replies, yet. This is very off-putting, I'm having a lot of trouble with GoG games as of late.

i have the same problem. did you ever find a solution? it works on my vista 64 bit laptop just fine. but it lags so bad it's unplayable on my windows 8 64 bit desktop.

Have you tried one of the beta versions available on the official site?
(which you can download after registering your serial key... it's in your GOG game page)

Is the game running slow itself when pressing aby button? Or is the speed of game all right but just that everything happens much later than they are supposed to?

When a key is stroke or mouse is moved, Windows sends and event to the current thread (to Unepic) saying "hey! the player pressed this key" and then Unepic moves the chararcter or whatever. This happens intantaneously.

In your case, lookd like this event is taking a looooooong time to arrive to Unepic. This is not normal, even for the oldest computer ever. There must be something else interfering, maybe another process (another software installed).
Try to close non-typical programs you have running in your computer, one of them could be the responsible.