Doesn't look too bad. Yeah, that was a warning chomp. Looks like it snagged the skin right above the nail - when that splits it bleeds a lot, and yes you should clean it - animal bites can get infected - but I've done worse to myself.
The dog we had when I was a kid was a champion warning chomper. He'd gnaw - usually closing down two or three times really rapidly - on you just hard enough to leave a dent, not even break the skin, and then get this smug attitude. Hurt like hell.
He was kind of a nuts dog. But then, we were evil little kids, so it all worked out. When we both got older, things calmed down and we were buds.