Where can I download a digital Starcraft II copy?

You can download it directly from your Battle.Net account.

https://eu.battle.net/account/management/download/#sc2-downloads

Click on the Windows or Mac button to download.

(You can even change the language if you want. I bought the French version but was able to download and play with the English version.)

Go to www.battle.net and login with your Battle.net account, You should be able to re-download from there.

Under My Games, just click on the SC II boxart, and select Manage Game. There should be a download link.

Log into your account at www.battle.net and go to "Account -> Your Game Accounts -> Starcraft II". There, you will find "Download Game Client"