It's always "or else" when used as a conjunction in modern English.

"Take your coat or else you'll regret it."

"Hurry or else you'll miss the bus."

Etc.

> if something is true, then do a thing, else do a different thing.

> That's just English, right? Except that it isn't

No, it is English, grammatically correct English. It's not idiomatic English but it's a perfectly fine sentence otherwise.

Idiomatic English would simply require adding an or

    if(x)
        do m
    orelseif(y)
        do n
    orelse
        do o

But of course a native English programmer would quickly recognize the or is redundant even if it is idiomatic, and drop it.

> I think a carefully-chosen German word was probably translated as an archaic English word and then never revisited

This is a weird reach. Else isn't an archaic word.

"Eat your dinner or else."

"If you don't do it someone else will have to."

Plus all the "or else" conjunction examples.

It was probably chosen because it was shorter than "otherwise" and not for any other reason.