I'd like to say yes but all modern fps shooters of that genre can trace back to halo, however the problem which COD created was that them made too good of a game too fast, call of duty 4 was good, however the problem which infinity ward had now was that they kept making the same game over and over again, creating a bad name for themselves even though their sales were good.
Treyarch on the other hand has been trying new things, zombies for example trying to keep the franchise and quite possibly the genre alive, however because of infinity ward they have been given bad press, another example of this situation is with most new games, if it's not the "big corperation titles" which are pretty much grey sludge poured out by executives and such it will always end up as a not bad but highly dull and un-imaginative game.
Leading on from that the other issue which call of duty has is the fact that "age restriction" means whine to your parents enough and you "WILL" get what you want, a bad trend in society. COD kids are a plauge on the gaming cominity as they have no respect for other players, whine, rage and are far too immature for games aimed at a matuture target audience.
And that is what call of duty is doing, along with other "big name" game franchises, grey corprate game slugde. However, there is still hope!
There are several names which have since survived the cod stain on the market, those being that of valve, counter strike, half life as well as other titles such as far cry, saints row, the list goes on. Furthermore the trend has been traveling away from that genre for a while now, people more interested in playing indie titles and "good" games which the only thing to do is "run around holding the fire button"
(even though that's pretty much minecraft but slightly tweaked.)
So... long boring pointless thing over, call of duty isn't killing the FPS genre, but it put it on life support, it can still recover if it had some imaginative new elements implemented.