Right! For sure.
But according to https://www.vice.com/en/article/xwqjg3/the-complete-untold-h...
It was already an FPS by 1998, 2 years before Microsoft was involved, and a year before the video shown above.
They started as an RTS, then decided it was way too much fun to actually drive the vehicles, and the rest is history.
Microsoft definitely helped with the development, but Microsoft bought a FPS game, not an RTS one.