i know this is almost a semantic issue to some, but i'm with balto on this issue.
this fight was clearly consensual - both parties meet unarmed at a mutually agreeable location and time to see which one is 'right' in whatever argument they were having. while it was clearly a serious fight and each guy was trying to fuck up the other, it wasn't what would legitimately be considered 'self defense.'
self defense occurs when one guy absolutely doesn't want to engage with the other guy but is forced to by circumstance (not just because you don't wanna look like a chump in front of some ladies).
most encounters that would qualify as self defense initially just end up as brutal assault and battery because of a disparity of force or initiative. an example would be a guy stepping away from an ATM and checking his wad o'cash to be sure it's all there, so focused on counting 20s that he never sees the guy who dings him in the grill, knocks him down, gives him the boot a few times and walks off with some cheese. it's hard to classify this as self defense because it's so one sided, but ambush situations make up the vast majority of criminal assault.
one of the reasons i train is because i got caught in a classic 2on1 ambush years ago - late night bus stop, one guy asks what time it is, his buddy clobbers me in the back of the head. i get staggered and start doing the herky-jerky-almost-falling-on-my-face kinda run to get away and they end up tackling me. i end up with some kinda fucked up headlock on one guy and the other guy is on top of both of us punching me until i let go. at some point in there, the first guy stabbed me in the inner thigh with something pretty short i guess - big cut but not too deep. they gave me a few kicks for good measure after i let go and took off with my wallet. i never saw the knife and didn't know i'd been cut for several minutes. i was too amped from adrenaline/shock to adequately assess myself. someone else who came to the bus stop pointed out the blood to me.
all told, about a doz stitches, 2 cracked teeth that ended up coming out, a broken rib or two and a coupla dislocated fingers.
on the other side of the coin, when i was in high school, guys would go out by the tennis courts at lunch and fight in much the same manner as those dudes in the vids above. basically over imagined grudges or girls and for nothing more than bragging rights. this was back in the late 80s before anyone knew what the hell MMA was, but it didn't look a whole lot different from these vids. i got beat up there, too
in any case, two completely different confrontations.