In my case under Firefox it does fail, but that is indicated with a tiny yellow triangle that is easy to miss if I'm not looking for it. Possibly something is different in your case but I'm guessing it is just Chrome not showing the error for some reason. I did also once get a .exe with a failed signature check that I'm guessing is the same issue, so I don't think it is strictly .bin files (but seems more likely to happen with larger files).
neumi5694: Actually Firefox CAN resume aborted downloads and it also signals when a download was aborted, depending on the server.
I did a quick search and see mentions that it can sometimes resume when you click retry, I guess that is what you mean? I didn't know that. It doesn't work on GOG, unfortunately, not because the server doesn't support ranges (it does, that is how curl was able to resume and I checked that this is still true on the current CDN) but because it retries the redirected url rather than the url of the link you clicked on and the redirected url no longer works (token expired). It deletes the mostly downloaded file instead, tries to download it again, then fails.
I saw another trick to move the incomplete .part file elsewhere, start the download again, pause it, move the previously downloaded part file back again, then resume. However, it seems pause and resume don't work with GOG either, although I don't know why since in that case it can restart from the beginning and download the full file.
However, I noticed that there are no cookies used for the CDN, just the time limited token (not single use) so it also works to start a download in Firefox, cancel it right away, copy the URL, and use it in curl with --remote-name (doesn't even need --remote-header-name that seems to interfere with resuming a transfer for some reason, however curl doesn't do URL decoding of the name so you also need to use deurlname from renameutils or similar). To resume a partially downloaded file from Firefox on a unixy system (I guess Chrome would be similar but I'm not sure exactly how it works):
1) move <file>.part to a new directory
2) restart the transfer in Firefox, cancel right away, right click on the download and select Copy Download Link
3) in the new directory run: curl -q --tlsv1.2 --proto =https -C - -f --output '<file>.part' '<url>'
4) mv '<file>.part' '<file>'
Something similar should work on Windows (recent Windows even comes with curl, but in PowerShell you need to run it as curl.exe to avoid an unfortunate alias).
Thanks to this thread I also did a check of my already downloaded files and found only one additional issue beyond what I had already noticed, which I think might be a different issue since the file wasn't just short but also had some incorrect content towards the end. At least I think I compared some of the short files and they were just short, although I'll look more carefully if it happens again.
It turns out that innoextract --test doesn't helpfully tell you what file has an issue if you are testing a bunch of them so I used:
fd -g 'setup*.exe' -x echo '{}:' \; -x innoextract --test --gog --silent
And for the linux ones I used the handy
xe utility (since somehow there was an extra newline in the middle of the script output when using fd, no idea how that happens :/):
xe -as 'echo -n "$1: "; bash "$1" --check' -- *.sh
Seems like a good habit to test them after downloading.