points go down when one team has control of more points than the other team. If your team has more than 100 nexus health, whenever a death occurs you will lose two nexus health. Similarly, capping a point will cause loss of nexus health, as can be seen at the beginning of the game. Thats pretty much it. At the time you referred to, green team has the left two, red team has the right two, and no one has top, so the number of points controlled is equal, so no one loses any.
Also, if you control say, 4 points to the enemies 1 point, or 5 to none, this will increase the rate the nexus goes down.
edit: fdru said 125 on the kills/caps thing, my info may be outdated as far as the 100 goes, i'm not sure.