It is based on the province's interpretation act (or their version of it). Some provinces are "opt in" provinces, meaning that if they want an act to apply to the crown as well, they need to explicitly state it does. If the act is silent, then it does not apply. Other provinces are "opt out" provinces, meaning if they want the act to apply, they can leave it silent, but if they want it not to, they have to state that the act does not bind the crown.
You are correct that the BC buildings Act does not specify if it binds the crown or not.
I was able to find a couple of BC acts that explicitly state that it does not bind the crown, so I would hazard a guess that BC is an opt out province, meaning that since the Buildings Act does not exempt application from the crown, The crown must comply.