This dispute is over the contract between Local One (the stagehands union), and the League of American Theatres and Producers (the organization that represents most of the Broadway theatres and producers). That contract sets out rules for how much the stagehands get paid, how many stagehands the theatres are required to hire, and other issues.
But some Broadway theatres are members of the League (and use that League-negotiated contract) and some are not (and use their own separate contracts). The theatres that are members of the League are the theatres owned by the big three companies — Shubert, Jujamcyn and Nederlander. Those are the theatres that are dark. (With the stagehands, Nederlander actually negotiates separately from the rest of the League, but they are standing firm with their League brethren in this dispute.)
The theatres that are not affected by the strike are theatres that are not members of the League. For instance, The 25th Annual Putnam County Spelling Bee is at the Circle in the Square, which is not a member of the League, and is on its own separate contract with Local One.
Cymbeline, Mauritius, Pygmalion and The Ritz are at theatres controlled by non-profit companies — Lincoln Center Theater, Manhattan Theatre Club and the Roundabout. They’re on what’s called a LORT contract, which typically governs regional theatres (these big three Broadway nonprofits have their own separate LORT contract especially for them).
Also still running is Xanadu, which is at the Helen Hayes, which is owned by Richmark Entertainment. Young Frankenstein is at the Hilton Theater, which is owned by Live Nation. Mary Poppins is at the New Amsterdam, which is owned by Disney.