As a lifelong native speaker (PNW English), I've also never heard "landed" used to refer to shooting down or capturing enemy airplanes. I could understand it from context, which is what I suppose the software is also going for, but I'd mark it with a red pen if someone showed me that sentence, just for clarity's sake (i.e. understandable from context but should be replaced).
These uses of 'land' and 'down' are military euphemisms for the use of force to compel a reluctant pilot to land. The difference is the degree of violence used.
Involuntary 'landing' implies the aircraft is forced to land by a party other than the pilot because if the pilot did not comply the plane would be shot down or collide or crash. It usually implies survival of the pilot. 'Downing' also means involuntary removal of the aircraft from the sky, but does not denote that a violent landing did occur, only that the likelihood of violence is much greater because a (more abrupt) landing was forced upon the pilot. From what I've read, 'downing' usually implies the plane crashed.