When installing the file "labw.exe", I get error saying "error moving the file".

When such things happen, try redownloading the installer, must be a download error.

Something else: Use the GOG downloader. When it finishes downloading the installer, click on the button "clear" and activate the download again. You will see the download bar filling up really quickly, which means that the downloader checks the files. Any possible errors will be corrected.

Tried both methods of installation, the same error occurs every time.

SHA 256 checksum for downloader acquired file:

Checksums for: setup_the_labyrinth_of_time_2.0.0.2.exe
SHA-256: 2c25e61d00c8ee10b90b5ed05b3295d72d4e3fc558bc7821dc9de16225ce4cef

SHA 256 checksum for directly downloaded installer:

Checksums for: setup_the_labyrinth_of_time_2.0.0.2.exe
SHA-256: 2c25e61d00c8ee10b90b5ed05b3295d72d4e3fc558bc7821dc9de16225ce4cef

Error I keep receiving (note that I tried various destination paths on different drives):
http://www.mujweb.cz/nakamura/gfx/labyrinth.png

I would like GOG staff to look at the issue, otherwise I will have to ask for a refund, which I consider resonable under the circumstances.

I have already submitted a proper report via GOG feedback system, including dxdiag and everything.

I can only add that I downloaded Labyrinth of Time from GOG a couple of days ago, and the installation went fine.

Real bugger you still have the issue.
At any rate, write GOG a support ticket, especially as this is a game-specific forum, and the chance of someone from the staff seeing this problem as opposed to it being mentioned in the general forum might be significantly lower.

Disable your AV/Security software during install.

Why should such a thing be necessary? All other dozens installers from GOG work just fine.

Because a MoveFile failed; code 2 error is, IIRC, your POS AV software deleting/quarantining the .exe in the middle of the install, unless that's a code 5. Why ... heuristics. To be fair pretty much all AV software has done something similar at one point or another.