I'm very picky about my gaming mice.
In terms of how important it is to be an actual "gaming mouse". My answer would be not very. That's kind of just a title sellers give stuff. What really matters is how it feels and how well it works. So with that in mind my suggestions while mice shopping would be.
#1: Do NOT use a wireless mouse (just in general, really).
I'm sure people do but for gaming you want responsiveness and wireless mice do not do that. No matter how expensive a wireless mouse is or what it can do there is going to be input lag because wired is simply faster than wireless. I mean, even if you owned the fastest car in the world would it matter if the speed limit was 25 miles an hour?
#2: Find one that feels right for you
Your going to be spending hundreds of hours with this thing in your hand. So make sure it feels right. What "right" is varies from person to person. It depends on the size of your hands. Whether your left or right handed(which effects which side of the mouse you want extra buttons to be on). Even how heavy or light you want it to be.
#3: Figure out how many buttons you want
I personally never use more than 6. Any more than that is what the keyboard is for, IMO. But some people like 10 or more. It's all personal preference. Aim to get whatever suits you.
#4: Don't overpay
There are some advantages in more expensive mice but those are really fairly negligible. I use a $40
Logitech G300s. It's an ambidextrous mouse, even though I'm right handed, which I like because I prefer having buttons on both sides of a mouse. It's fantastic for my tastes. And works flawlessly for gaming.