necesse is a predicate that, in this case, takes a subject clause. We tend to render these subject clauses in English either as a "that-clause" like indirect discourse [that the possessor is happy] or as a gerund phrase [the possessor being happy]. 

The subject is "qui potiatur sit beatus."

All of this is in a relative clause introduced by quo, which is correlative with id. 

That thing alone would be good, by virtue of which (quo) it would be inevitable (necesse sit) that the one who should possess it would be happy (qui potiatur sit beatus). 

Or: 

That thing alone would be good, by virtue of which (quo) the one possessing it being happy (qui potiatur sit beatus) would be inevitable (necesse sit).