Hi!
I have Ubuntu 20.04 and I tried running SC2 with this install and it didn’t work either.
What worked for me was this video on youtube:
search by this name: “How to install and run starcraft II on linux - lutris, blizzard batllenet, gpu and wine” uploaded by intelligent gaming (the page does not allow me to leave links).
This guy explains all the steps to follow, he even leaves the links on the pages to download everything.
- Install the graphics card drivers
- The installation Wine from the official website.
- Install Lutris.
- Install battlenet
- Install SC2
Now battlenet and SC2 open directly with the Wine application.
I imagine that to download the other games it must be the same until step 4.
Hope this can help you.