I don't know that it should be called a "gyro", but I'm sure it is still good.
Gyro meat is traditionally made from ground meat with added spices, then that meat is formed onto a stick that is spun like a rotisserie style to roast it. I wouldn't take too much offense if it was simply formed into loaves and roasted that way because the flavor would still be pretty much identical.
For me, the deal breaker with using ground meat that you simply cook up in a loose meat fashion is that the texture would be different. That would be the biggest difference. The change from roasting a hunk of formed ground meat to either pan/griddle frying a bunch of ground meat or simmering it in a pan can affect flavor as well.
I have seen Gyro Burgers before, where the meat is formed into a patty, grilled and that patty placed in a pita and dressed like a standard gyro. I don't find the term "Gyro Burger" bothersome, because it describes it well. I honestly am not sure what to call simply cooking up a bunch of loose gyro meat, but it seems a bit deceptive to just put that in pita with standard dress and call it a "Gyro". Some description should be used to signify the difference.
All just my opinion, which based on past experiences isn't worth much in today's economy.