Old Blizzard games at least don’t need the internet to install and play, stuff like Diablo 2 and even Starcraft shouldn’t. For offline play even the serial doesn’t matter, because it’s not checking against some online database or something. Only once you go online do you need your own personal CD key, that’ll be tied to an account.

Once you get to later installments of these series you get entries that either need a constant internet connection or and occasional check, like Diablo 3 onwards, the Diablo 2 Remaster and maybe Starcraft 2 as well.

It’s weird that your Starcraft version needs an internet connection for the installation. I don’t have that tied to my Battle.net Account, but I do have Warcraft 3 and Diablo 2. So I just downloaded those and did a quick test without internet, and they installed without issues. Yes, it’s not the same as directly from the CDs, but it would be weird if the “modern” download was more convenient than the old stuff. I downloaded a downloader, that then downloaded the actual game. I remember stuff like that in the past as well, but maybe only for patches (and definitely World of Warcraft).

I might have some old CDs of these games as well, but they are buried in some boxes, stuck behind other stuff, so I can’t quickly check if those are the same.