::::That's an interpretation. And state and nation are inseparable under the Spanish constitution (1978) that only accepts the term nation for Spain. 
Wanting to keep Spain united is legitimate but, specially as this is done via denying the right of self-determination for minority nations such as the Basque one, it clearly is Spanish nationalism.
Part of the problem may be that "nationalist" in Spanish has not the negative connotation that may have in English. Instead "patriotic" does have a negative connotation in Spanish that doesn't seem to have in English. They are sort of inverted in their shades. But basically they mean the same thing after all. 
Nationalism is after all the ideology that supports the ambitions of certain nation (nation-state, stateless nation...), often at the expense of others. It's not very different from patriotism actually but somehow people seem to feel differently about these terms and the feelings are opposed in English and Spanish. In Spanish "patria" (fatherland), "patriota" and "patriótico" are part of the language of the Army, which is inherently associated to Francoism and other many military coups. Franco and his partisans abused these terms mercilessly, so Basque nationalists almost never call themselves "patriotas" in Spanish, even if that's the literal translation of "abertzale" but "nationalists". On the other hand Spanish nationalists (PP, PSOE, some minor parties) don't use either term normally but talk about the unity of Spain and not being nationalist (in the sense of stateless nations' patriots). 
Also, back to the PSOE, they have a somewhat confuse discourse but, outside of Catalonia, they are clearly centralists. Navarrese PSN is as anti-Basque as UPN (PP). Western Basque PSE-EE is, despite its incorporation of the acronym EE, at most very limitedly regionalist. 
Under PSOE governments transference of attributions as per the Gernika statute were frozen almost totally most of the time. Their discourse may be somewhat confuse but they are clearly against Basque self-determination and self-rule beyond what is almost unavoidable to keep some appearence of social peace. They are not as extremist or inflexible as PP maybe but that only makes them moderate Spanish nationalists, but Spanish nationalists anyhow. 
PSOE is also strongly in the Jacobinist tradition that all pan-French parties have. Yet the reality of Spain doesn't fit so well with those centralist premises and therefore an unstable arrangement had to be made. It was nevertheless more impelled by the extinct UCD of Suárez than by the PSOE itself. And it's understood by most that the coup of 1981 was a whistle blow, with the complicity of PSOE, against "excessive" decentralization that Suárez seemed willing to concede. 
Whatever the case, the term "unionist" seems to avoid all this problematic and is a good English term. I really can't find anything better. My POV is "Spanish nationalist" as more precise term, "unionist" is for me a linguistic compromise and also a step towards NPOV. 
I'd really like to hear from Mountolive. He's not said a single word.