Splatoon kind of plays like a shooter, but the point isn't to shoot other people. You can shoot them if you want, of course, whether it's to get them out of the way or just because you're sadistic, but taking out foes in the four-on-four matches isn't going to lead your team to victory.
That didn't stop me from shooting half-squid-half-kid hybrids from the opposing team every chance I got. I'm just saying, it won't get you the win.
No, to win you have to cover as much of the level as humanly (squidly?) possible with paint. That's what you're shooting: not bullets, but very colorful paint. Each team has its own color, so you can tell where your territory is marked and where you need to take over. The GamePad screen gives a top-down view of the level, including where the other characters are and how the paint is falling, but it's hard to pay attention to that screen when there's so much action happening on the TV screen.