Slight expansion - Microsoft have the rights for any and all computer expression of the Battletech IP. This means not only games, but design programs, electronic record sheets, etc.
We don't know that. Remember legality is rarely known until a court case settles it. Especially when the current people involved were not the ones that made the agreement and the agreement is old. We know that the various parties have acted one way. If you had asked what book rights were 20 years ago, you'd get a definitive answer. Then digital publishing hit and we got all sorts of answers on how those rights were affected by long standing agreements. Sometimes writer kept digital rights, because they were stipulated in the agreement. Sometimes the writing was given to the company, but the artwork was not given (for digital use). It threw everyting in the air. What was true 20 years ago re: Microsoft's rights may be interpreted very differently now, where some sort of digital technology is heavily involved in many tabletop games. Clearly MS's rights don't limit CGL having a BattleTech website. Does it affect the master unit list? Does it affect the MUL having AS unit cards available? Does it affect the MUL allowing players to select units and make a list to print? Does it affect the MUL allowing players to construct their own units, using the in print game rules, and print their own AS unit card for it? Would you give the same answer for other games? Does Warmachine having a computer game make Privateer Press unable to make digital aids for its own game? Can you think of any other tabletop game that then has a computer game, where the tabletop game is then unable to make digital aids for its own games?
Of course, there could be something in writing from FASA saying otherwise, but I'm not sure anybody has seen it (including CGL). it's all guesswork and how much does CGL want to push back. Oh wait, push back against Microsoft... There's the last puzzle. Legality goes to the one with the best lawyers..
Rick Raisley of HeavyMetal fame used to have to pay licencing fees to MS back in the day (I suspect he may not be doing so now, due to low volumes).
As far as I know, it was a one time fee. And no term limit.
Sites like Sarna, and teams like MegaMek, could technically be hit by MS lawyers, but MS is unlikely to do so as there's no money, and they're not competing with MS per se. Pihrana had to license from MS, then Harebrained licensed from them - or vice versa, not quite remembering - but then it's pretty much as above.
I don't know of a single court case where a tabletop game has had to stop making digital aids because the computer game rights are with another company. Of course, there may be a specific agreement for BattleTech, but considering when that agreement would have had to be made (at or before FASA Interactive split), I don't think anybody was going to specifically refer to digital aids for a tabletop game. MegaMek is on pretty shaky waters, I agree I don't see anything saving that but MS not caring. But Sarna? I don't think MS could go anywhere near it. Topps on the other hand? The probably could.
Final note, I took a class in Business Law. So I am dangerously ignorant.
TLDR: We don't know what is legally binding on anybody. We have some idea how it has worked out in the past.