Yeah, it as alot of "pop". Sounds somewhat dry, and with some "airy" overtones (you might call that ring). But I wouldn't muffle it (personally) because it isn't too "saturated" or "wet" and you would just end up killing the sound (most likely). But I think it sounds really good.
Let me guess, do you crank the bottom (Resonant head) really tight?
Let me also guess, does it have a Die Cast hoop (at least on the batter)?
I have a snare that sounds pretty much identical to yours. It has an ambassador coated batter, and Ambo Reso snare side...nothing special, but it works!
Also, I don't know who, what, when or how you recorded this, but Pure MAGIC can happen if you know how to use a good compressor on your snare drum.
Btw, don't take offence, but as a guitar player I feel qualified to comment on the song. Your guitarist needs to get a fatter sound, and it sounds way too flat, and almost like he is playing through a harsh-sounding solid state amp.
I think since the guitar sounds a little "wimpy" in the mix, and bass sounds a little muddy in the mix, naturally listeners ears are going to focus in on the next loudest thing...the snare. In other words, your snare is going to "appear" to be louder. Thus this "Ring" will be more easily heard in a recording. Just my theory. Good playing though. And really nice Drum tones I'm hearing.
P.S. sorry for the Honesty.