The biggest effect this will have is on government employees that I see, is on those that live in the Maryland suburbs out toward BWI. Officially, one is suppose to compare surronding markets and take into account travel costs. For instance, for my BWI based friends they typically face situations like, 300 dollars total fare from BWI with a 20 dollar cab ride= 320 dollars. 250 from IAD with a 100 dollar cab ride= 350, 300 from DCA with a 50 dollar cab ride=350 total. In this situation they can fly out of BWI because the total expenditure is the lowest in absolute terms (including all transportation ). Additionally, they save a lot of time, which only matters if it is during the week (at least at my agency we do not get compensated for weekend travel). With WN dropping out of the BWI bidding, it is likely that government fares will rise considerably, which will likely change the total cost calculation and cause people to have to fly out of IAD and DCA more often.

Keep in mind that the "cheapest airport option" is very much an agency specific policy. Also, one may book a non contract fare if it meets the qualifications of the GSA contract fare (read as a fully refundable ticket) and some other factor (such as cheaper or more convenient). Thus, it is unlikely that that WN will lose all of its government business, it is just that that business will be on their prevailing refundable fares.