No, absolutely not. That translation is incorrect! I propose 'the complete opposite' or 'the utterly alien'. 'The wholly other' is a bad translation and the OP is right to question it. There are many bad translations out there, and this is one of them. For decades I have seen translations of wir andere by Nietzsche as 'we others'. Nonsense! 'The rest of us' is a correct translation, but 'we others' is certainly not!
If you think about it, you should realize that 'other' cannot be a matter of degree, and thus 'wholly other' is ludicrous on its face. Something cannot be more or less 'other', partially or wholly 'other'. In fact, no adjectives can be applied to 'other' at all! It's not qualifiable! It's absolute! It's like 'dead' in that sense, an absolute adjective made into a noun ('the dead are all around us').
See: absolute adjectives
This means that the German word andere here cannot mean 'other' but must mean 'different', 'strange', 'alien', or something of that kind, something which can be qualified and modified. How can such idiotic translations even see the light of day?
Here is an idiomatic sentence using 'other':
'Where are my gloves? Oh, here's one, now where is the other?'
It does not appear in the 19th century, which proves it is not an idiomatic expression. As a literal translation, it is pointless and absurd. Too much if this kind of thing is still going on, and I commend the OP for bringing this horrible translation to our attention. Ganz doesn't mean just 'whole' or 'wholly', and andere doesn't mean just 'other', as can be seen here: