Well, that's what makes me curious! They have a class that runs the BIST parser (by Kilperwasser and Goldberg) using spaCy to pre-process for tokenization, sentence boundard detection and POS tags. Now, spaCy by default uses the parser to add sentence boundaries...So you've already got a parse right there.
So, is their BIST parser more accurate than spaCy's parser? I'm getting similar (but slightly higher) WSJ accuracies to what Eli and Yoav reported in their paper, so I'd be surprised if they're doing so much better?