I don't know how the Game of Thrones reference originated but it doesn't fit at all.
Both settings inspired by European history, especially the War of the Roses and the Hundred Year's War? Check.
Both settings are about the dynastic struggles between feuding Houses over a vacant throne? Check.
Both settings add magic? Check. (don't kid yourself, interstellar travel and mecha are just a different brand of magic than dragons and zombies)
Granted, if you came in to BattleTech after it jumped the shark with the whole "MunchkinTech" revolution of the Clan Invasion era, you may have never played BattleTech when it was Game of Thrones in Space. But in the 3025 era, as the OP is asking about, it was. Once upon a time.