Yes, obviously, they have monopsony power because networks are natural monopolies. The problem is that they can extract rents because of that monopsony power... and they do.
Because it's convenient to have all buyers operating through a single network, that network has the ability to extract rents from the sellers. It should be trivially illegal to operate such a site in the US, given anti-trust laws, but we've decide in the last 40 years that we don't enforce anti-trust in the US anymore, so here we are.
The fact that sites like booking.com can charge hotels a commission of up to 25% per booking shows exactly the level of extractive power that a site this type of power, simply because they were the first to capture the monopolistic network. It doesn't matter that some of the smaller hotels and course will go out of business, even if customer as a whole are hurt, because the total market is more valuable to them by maximally extracting rents.