Since black holes are considered points in space,
Well, the singularity at the center of the black hole is a point (or, is a point if the black hole isn't spinning.) The term "black hole" refers to the event horizon and everything inside it. The stuff inside is not observable-- the math says it's a singular point (ignoring quantum mechanics, since there is no theory of quantum gravity), but that's not observable.
Technically, when we say it's spinning, the actual meaning is "the black hole has angular momentum." The word "spin" is just shorthand. Same goes for elementary particles, for what it's worth. An electron has spin, but don't think of it as having some part of it is moving in circles.
are they still considering spinning black holes (which is essentially all of them) "ringularities"?
Yes, the singularity at the center of a black hole with nonzero angular momentum is theoretically not a point, but a ring.
And it would seem that angular momentum is likely to increase with each merger, since they're going to tend to orbit each other in the plane of their spinning?
Could go either way, depending on whether the angular momentums of the individual black holes, and the angular momentum of the two holes orbiting each other, are aligned or anti-aligned. Also, the gravitational radiation of the merger carries angular momentum away, so the angular momentum of the merged system is less than the (vector) sum of the angular momenta of the two individual black holes and the orbital momentum.