None of the other options work. Not play-it, not the gog-risk-of-rain AUR installer, obviously not the .sh GOG bundles which only officially supports those ancient Ubuntu versions, so I will create a new post with all I needed to do to even open this buggy game. I will squash this now, the GOG version does not have bugfixes over the Steam version. If you want to play this game know that you CANNOT play any loops or with the artifact Honor (the game crashes when specific elite mobs spawn), play on servers with other people (anyone can pick up spike strip) and finally cannot unlock all the characters without cheating.

So I will compile all the errors I encountered so this is easy to find in google and the steps I used to fix them.

Install the game;
chmod +x ./gog_risk_of_rain_2.1.0.6.sh
./gog_risk_of_rain_2.1.0.6.sh

Once installed, go to the install directory in your terminal and run ./start.sh. You will get all of the following errors;

./Risk_of_Rain: error while loading shared libraries: libcurl.so.4: cannot open shared object file: No such file or directory
./Risk_of_Rain: error while loading shared libraries: libcrypto.so.1.0.0: cannot open shared object file: No such file or directory
./Risk_of_Rain: /usr/lib32/libcurl.so.4: version `CURL_OPENSSL_3' not found (required by ./Risk_of_Rain)

Fix them all by installing;
sudo pacman -S lib32-libcurl-compat lib32-openssl-1.0

And running the game like so;
LD_PRELOAD=/usr/lib32/libcurl.so.3 ./start.sh

There are far more errors printed again but nothing game breaking (at least, it plays and crashes exactly the same as the Steam version no less no more).

The games files are all stored in ~/.config/Risk_of_Rain

I'm just coming by to say thank you, dear sir.

For all those who are, like me, linux noobs and too lazy to type out the LD_PRELOAD command every time, you alter the something in the "start.sh" file:

When you open "start.sh" with the editor of your choice, you will find this code block:
# Actions
run_game() {
echo "Running ${GAME_NAME}"
cd game
./"Risk_of_Rain"
}

now, after installing the packages OP has mentioned, you simply add the "LD_PRELOAD" command OP was talking about IN FRONT OF './"Risk_of_Rain".

Thus, your altered block should look like this:
# Actions
run_game() {
echo "Running ${GAME_NAME}"
cd game
LD_PRELOAD=/usr/lib32/libcurl.so.3 ./"Risk_of_Rain"
}

Again, thanks to OP to pointing to a fix!

greez labuvetteducampus