How can I get my Steam Cloud saves without installing the game?

I currently started a new game on Saints Row: Gat out of Hell from GOG. Since you can import your character from the old Saints Row 4 savegames, I need my data that is stored on Steam Cloud.

Because I don't want to download the whole 9+1 GB of SR4 on Steam just for the saves: How can I get my savegames stored on Steam Cloud without having the game installed?

This should now be possible through https://help.steampowered.com/en/accountdata thanks to GDPR, at least in part. Specifically the Steam Cloud link under the section "Uploaded Data".

You can download the files one at a time from here: https://store.steampowered.com/account/remotestorage

Or you could just download the game, synchronize it and then move the files.