They would have probably received more money over the next 4-5 years from letting MASN run the course than they'll get on the open market.
Local MLB TV rights are almost worthless right now. They're best long term bet is if MLB is still trying to package multiple local rights with other teams to sell to someone like Netflix/Apple/Amazon. Leonsis still seems to think that local TV rights on RSNs are still a viable model, and gets to play with Middle East money so, there is a chance he overpays, but he's not going to be bidding against anyone else in the RSN space.
The rights are probably only actually worth 5-10 million/year in a post RSN bubble market.
My guess is the options are:
1. Sell as part of MLB package to Amazon/Apple/etc.
2. Sell to Monumental for an overpay - 30-40 million/year. That's not sustainable without foreign subsidies though, so could all bankrupt in a couple years.
3. Monumental bids what they're actually worth at <10 million/year and Nats have to decide whether to take it, or go with the stop gap MLB produced MLB.tv deal like the Padres have that likely wouldn't pay much more. Probably preferrable to go with the latter and hope they can be early participants if the MLB streaming package gets going later.
None of these will be a financial bonanza for the Nats, and will actually be a short-medium term loss of revenue. They'll be in the same boat as most of the other teams though at least.