This is a somewhat literary sentence construction, almost like the start of a story, but while it is slightly dramatic it's not uncommon.
"Theirs was not exactly a textbook friendship," is equivalent to, "Their friendship was not exactly textbook," and so friendship remains the subject of the sentence. The second part of the sentence describes why the friendship was unusual.
I wouldn't say it's an example of a split subject as you reference. Those seem to require a repetition or duplication of the subject, used in vernacular, and not "correct" formal English. Your example is, however, grammatically correct.
Another example of the same type:
Theirs was a terrifying beast, not so much a tomcat as a Machiavellian demon whose astounding technique for soliciting food involved equal parts obsequiousness and extortion.
Although the language is picturesque, the subject is still "their cat". Another:
His was not a great work of art, but merely the best a humble artisan could produce with the tools he was given.
The subject is "his art", not great art but still not bad.
One more somewhat related example (mostly for fun). You can't get more literary than Dickens' "A Tale of Two Cities":
It was the best of times, it was the worst of times, it was the age of wisdom, it was the age of foolishness, it was the epoch of belief, it was the epoch of incredulity, it was the season of Light, it was the season of Darkness, it was the spring of hope, it was the winter of despair, we had everything before us, we had nothing before us, we were all going direct to Heaven, we were all going direct the other way – in short, the period was so far like the present period, that some of its noisiest authorities insisted on its being received, for good or for evil, in the superlative degree of comparison only.
Here "it" means "the current time", although here (in contrast to your example) Dickens uses repetition of the "it was ..." to suggest what the times were, instead of writing a more clear description.