Darvond: Certainly, but that doesn't account for things like one time authentication, handshakes, and other annoying factors.
vv221: I did not check in details how lgogdownloader does it, but of course any authentication process is done again on the download resuming. This is technically a new connection.
None of that matters. As long as you're able to start a download and the server supports range requests, you could move to Uganda, buy a new computer, drop your old interrupted download on it, create a new account on GOG, buy the game you already had, and resume that old download.
The whole point of the range header is that you can open a new connection and continue a download (and less commonly, seek in a media file). Historically, HTTP has very much been a one-connection per request kind of protocol (pipelining is supported in HTTP/1.1, but rarely used). There would be no point having such a header in the first place if you couldn't use it on a new connection.
Authentication is just cookies.
(I just tested this, started a download using wget and finished it on a different computer using curl)
I guess it can use the size of the already partially downloaded file
Exactly! This is how curl, wget, ftp, etc. work. And so does lgogdownloader:
https://github.com/Sude-/lgogdownloader/blob/4997a455970f017b700267f4a514262d200cafcc/src/downloader.cpp#L1038