Adverb "other (than)"

'Other' is an adjective, but 'other than' is an adverb phrase that's modifying the adjective.

So, 'Other than' being the adverb that it is, acts upon 'to be.'

But 'other' by itself can't be linked as an adverb 'to be.'

What they mean by a bit of both is maybe...

Other connects with 'marriage' as an adjective.

Other than connects with 'to be' an adverb.

It never occurred to me ours would be other than a marriage in name only.

"Other" is an adjective with the preposition phrase "than a marriage in name only" as its comparative complement. We know it's a complement because it's obligatory.

The whole adjective phrase "other than a marriage in name only" then functions as predicative complement of "be".