I don't know much about trademarks. However, I do have some patents. I do know this with patents, if the patent holder knowingly allows someone to infringe on the patent and doesn't do anything about it, soon they will have no patent or the patent will be unenforceable.
Win or loose, BNSF may be in the position where they have to sue to maintain rights. If BNSF knowingly allowed and entity to use the Northern Pacific name without challenge courts may take that as abandonment of the trademark.
While both of those statements are true (basically if someone doesn't defend copyright or patents or trademarks, it is assumed that basically they no longer are claiming that right) there is a big difference with this lawsuit, and that is that copyrights (or even patents for that matter) are very specific. The issue with Northern Pacific Airlines is that the "Northern Pacific" BNSF has was with a railroad, not an airline.
To give you an analogy, back in the dark ages of automobiles, a lawyer by the name of Selden (Seldon possibly) bought the patent of an engine that an inventor whose name I think was Bray, and he created a mess in the automobile industry around the turn of the 20th century. Some manufacturers licensed the Selden patent, and they had an association that was the 'licensed automobile makers" (I believe the NY auto show has it roots in a show this group put on around 1900).
Other makers, like Ford, refused, and it went into court. And what the courts ruled was the Bray patent was specifically for a 2 stroke engine of a specific design, and unless the engines in cars being produced were a)2 stroke and b) noticeably the same as the Bray design, there was no infringement.
If BNSF owned the rights to a defunct airline called Northern Pacific Airlines , then it would be trademark infringement. Even assuming they own the rights to "Northern Pacific Transportation", that is so broad it could be used to for example stop a car maker or a bike maker from calling something "northern Pacific", or even in its most wild, sneakers or shoes (since they could be construed by a crazy lawyer as transportation).
If BNSF sued claiming that use of the name diluted the value of their brand (for example, like the greasy spoon called "4 seasons" with the famous restaurant) and issued cease and desist they might have a case, if the name was still in use as a a railroad and they argued it caused confusion (how I don't know, even that is a stretch). They aren't though, they are suing for licensing revenue which quite frankly is bogus, more than likely they want the airline to settle because of the legal costs of going to court, which a small airline may not be able to afford. In some cases of trademark issues like this, the argument was that even if it is an unrelated industry, that using the brand in question enhanced the other company. So for example, if the Northern Pacific railroad still existed, and it was a premiere railroad, they might be able to argue that the Airline by using that name picked up some cachet from people associating it with the railroad (it is kind of the 180 degree opposite of claiming that using the brand hurt the status of the plaintiff, like the 4 seasons thing). Since the NP hasn't existed for 50 years and as a brand might only impact people who remember the NP in its prime, pretty specious argument IMO. Again, it is revenue thing, BNSF figuring they can get the airline to settle rather than having to to go court, cheaper to settle in a lot of cases.