How do they get apartments listed with them and what are the legalities of such listings? And if the apartments are not their own, how much commission are they taking?
No, they clearly do not own any of the properties being offered. It says so right on the site if you look. They are both booking agencies. That's defines the liability. Revenue comes from membership fees (people pay an annual fee or initiation fee to join as tenants), from service fees per booking, and some commission from the property owners for arranging the bookings. The model is likely similar to many non-hotel accommodations. The difference is the minimum stay length. Every municipality has their own legal regulation of temporary accommodations. You would need to investigate the laws in each place you intend to represent a property. While companies like these used to shift the burden to the property owner, the trend has been to ensure compliance through the agency. Like online purchases now collecting state tax from out-of-state buyers (think Amazon.com), it's now part of the booking agent's diligence to ensure the property owners have the right permits and are paying the right taxes for running a business.