So same issue. The files are downloaded, but something seems to be going wrong.
DEBUG 2020-03-13 22:54:33,206 [downloader.on_done:97]:Finished downloading https://content-system.gog.com/products/1686426343/users/46989348093230870/namespaces/website/download?path=%2Fsecure%2Foffline%2F1686426343%2F1686426343%2F53002773575448699%2F6716%2Fsetup_a_hat_in_time_nyakuza_metro_1.12_%2864bit%29_%2835607%29-2.bin&token=eyJhbGciOiJIUzI1NiIsImV4cCI6IjE1ODQyNTEzMzQifQ.eyJjb250ZW50Ijoie1widXNlcl9pZFwiOjQ2OTg5MzQ4MDkzMjMwODcwLFwicHJvZHVjdF9pZFwiOjE2ODY0MjYzNDMsXCJwYXRoXCI6XCJcXFwvc2VjdXJlXFxcL29mZmxpbmVcXFwvMTY4NjQyNjM0M1xcXC8xNjg2NDI2MzQzXFxcLzUzMDAyNzczNTc1NDQ4Njk5XFxcLzY3MTZcXFwvc2V0dXBfYV9oYXRfaW5fdGltZV9ueWFrdXphX21ldHJvXzEuMTJfKDY0Yml0KV8oMzU2MDcpLTIuYmluXCJ9IiwiZXhwIjoiMTU4NDI1MTMzNCJ9.CHuAEvyc32bEXFWnp1Zh3U-gyfdQ-c8132TLKHq9Z0A&access_token=Oe7UVHAKUrryEdL6omcn1jF4mDVuIKF1jIJ2ysRc4ankWGqscpkyDLTCrxtdaUeNotnc-Hd-ybTV-2Zf7iuwL8lXNVz5CWnc3CCWawFk_DSMEI_IIZZIePyhg5DQGKgtKbuAvzWcKUmSZt6BYBwuyg
DEBUG 2020-03-13 22:54:33,676 [interpreter._iter_commands:573]:Installer command: {'task': {'prefix': '$GAMEDIR', 'name': 'create_prefix'}}
INFO 2020-03-13 22:54:33,677 [wine.create_prefix:99]:Creating a win64 prefix in /home/marmalade/Games/a-hat-in-time
DEBUG 2020-03-13 22:54:33,678 [system.execute:38]:Executing /home/marmalade/.local/share/lutris/runners/wine/lutris-5.2-x86_64/bin/wineboot
DEBUG 2020-03-13 22:54:33,678 [system.execute:44]:WINEARCH=win64 WINEPREFIX=/home/marmalade/Games/a-hat-in-time WINEDLLOVERRIDES=
INFO 2020-03-13 22:54:48,495 [wine.create_prefix:148]:win64 Prefix created in /home/marmalade/Games/a-hat-in-time
DEBUG 2020-03-13 22:54:48,528 [interpreter._iter_commands:573]:Installer command: {'task': {'executable': 'install', 'arch': 'win64', 'args': '/VERYSILENT /SUPPRESSMSGBOXES', 'name': 'wineexec', 'prefix': '$GAMEDIR'}}
DEBUG 2020-03-13 22:54:48,554 [wine.use_lutris_runtime:113]:/home/marmalade/.local/share/lutris/runners/wine/lutris-5.2-x86_64/bin/wine is provided by Lutris, using runtime
WARNING 2020-03-13 22:54:48,567 [wine.game_exe:543]:The game doesn't have an executable
DEBUG 2020-03-13 22:54:48,568 [command.start:112]:Running /usr/bin/lutris-wrapper 0 0 /home/marmalade/.local/share/lutris/runners/wine/lutris-5.2-x86_64/bin/wine install /VERYSILENT /SUPPRESSMSGBOXES
DEBUG 2020-03-13 22:54:48,568 [command.start:114]:ENV: WINEARCH="win64"
DEBUG 2020-03-13 22:54:48,568 [command.start:114]:ENV: WINE="/home/marmalade/.local/share/lutris/runners/wine/lutris-5.2-x86_64/bin/wine"
DEBUG 2020-03-13 22:54:48,568 [command.start:114]:ENV: WINEPREFIX="/home/marmalade/Games/a-hat-in-time"
DEBUG 2020-03-13 22:54:48,568 [command.start:114]:ENV: LD_LIBRARY_PATH="/home/marmalade/.local/share/lutris/runners/wine/lutris-5.2-x86_64/lib:/home/marmalade/.local/share/lutris/runners/wine/lutris-5.2-x86_64/lib64:/usr/lib/libfakeroot:/usr/lib/openmpi:/usr/lib32:/usr/lib:/usr/lib64:/home/marmalade/.local/share/lutris/runtime/Ubuntu-18.04-i686:/home/marmalade/.local/share/lutris/runtime/steam/i386/lib/i386-linux-gnu:/home/marmalade/.local/share/lutris/runtime/steam/i386/lib:/home/marmalade/.local/share/lutris/runtime/steam/i386/usr/lib/i386-linux-gnu:/home/marmalade/.local/share/lutris/runtime/steam/i386/usr/lib:/home/marmalade/.local/share/lutris/runtime/Ubuntu-18.04-x86_64:/home/marmalade/.local/share/lutris/runtime/steam/amd64/lib/x86_64-linux-gnu:/home/marmalade/.local/share/lutris/runtime/steam/amd64/lib:/home/marmalade/.local/share/lutris/runtime/steam/amd64/usr/lib/x86_64-linux-gnu:/home/marmalade/.local/share/lutris/runtime/steam/amd64/usr/lib"
DEBUG 2020-03-13 22:54:48,568 [command.start:114]:ENV: __GL_SHADER_DISK_CACHE_PATH="/home/marmalade/Games/a-hat-in-time"
DEBUG 2020-03-13 22:54:48,568 [command.start:114]:ENV: __GL_SHADER_DISK_CACHE="1"
DEBUG 2020-03-13 22:54:48,568 [command.start:114]:ENV: DXVK_HUD="compiler"
DEBUG 2020-03-13 22:54:48,568 [command.start:114]:ENV: DXVK_STATE_CACHE_PATH="/home/marmalade/Games/a-hat-in-time"
DEBUG 2020-03-13 22:54:48,568 [command.start:114]:ENV: PYTHONPATH="/usr/lib/lutris:/usr/bin:/usr/lib/python38.zip:/usr/lib/python3.8:/usr/lib/python3.8/lib-dynload:/usr/lib/python3.8/site-packages"
/usr/lib/python3.8/subprocess.py:844: RuntimeWarning: line buffering (buffering=1) isn't supported in binary mode, the default buffer size will be used
self.stdout = io.open(c2pread, 'rb', bufsize)
Running /home/marmalade/.local/share/lutris/runners/wine/lutris-5.2-x86_64/bin/wine install /VERYSILENT /SUPPRESSMSGBOXES
000b:fixme:winediag:__wine_start_process Wine TkG 5.2 is a testing version containing experimental patches.
000b:fixme:winediag:__wine_start_process Please don't report bugs about it on winehq.org and use https://github.com/Tk-Glitch/PKGBUILDS/issues instead.
0009:err:module:__wine_process_init L"C:\\windows\\system32\\install.exe" not found
Waiting on children
All children gone
Exit with returncode 53
DEBUG 2020-03-13 22:54:49,567 [command.on_stop:161]:The process has terminated with code 13568
DEBUG 2020-03-13 22:54:49,567 [command.stop:246]:Management process looks dead already.
DEBUG 2020-03-13 22:54:49,568 [command.stop:254]:Detaching logger
DEBUG 2020-03-13 22:54:49,608 [game.save:234]:Saving A Hat in Time (wine)
DEBUG 2020-03-13 22:54:49,609 [config.save:208]:Saving LutrisConfig(level=game, game_config_id=a-hat-in-time-gog-dxvk-1584165289, runner=wine) config to /home/marmalade/.config/lutris/games/a-hat-in-time-gog-dxvk-1584165289.yml
DEBUG 2020-03-13 22:54:49,632 [lutriswindow.on_game_updated:721]:Updating game A Hat in Time (wine)
DEBUG 2020-03-13 22:54:49,685 [interpreter._write_config:665]:Saved game entry a-hat-in-time (5)
WARNING 2020-03-13 22:54:49,687 [interpreter._finish_install:618]:No executable found at specified location /home/marmalade/Games/a-hat-in-time/drive_c/GOG Games/A Hat in Time/Binaries/Win64/HatinTimeGame.exe
I don’t know enough about how Lutris functions to really pick out anything here that looks abnormal, but as far as I can tell it seems to be an issue with downloading the files in the strange unnamed segmented format.