Rendering Intent is Abs. Col.
Profile is Epson's canned Epson 9800 for "Pro9800 7800 PGPP" read as Epson Premium Glossy Photo Paper.
It's a pretty good profile except at low L values where the profile is incorrectly made as they apply BPC to their AtoB1 and BtoA1 lut tables. This has little impact at L=50 though. The plots are very similar to Rel. Col. Intent at L=52. The same tables are used except that the values are scaled to the paper's white point instead of exact colors. Normally, gamuts are measured using Abs. Col. intent.
The black lines have a hue in steps of 10 degrees from 0 to 350. The position at each point on the black lines represents the actual hue (not saturation) of the printed colors when the requested saturation is as shown on the a*,b* location. The printed saturation is, of course, on the gamut boundary.
For instance, at the first 10 degree line the farthest point on the right is a requested color of Lab=(50,125,22) but the actual printed color is Lab=(48,79,10) which is an angle between 7 and 8 degrees.
Similarly, looking at the 80 degree hue line, the first curved line to the right of the 90 degree top, straight line, we see the outermost point is at ab=(39,121)which has a hue angle of 72 degrees. The actual requested color is Lab(50,22,125) with a hue angle of 80 degrees.
The way to look at what the black lines means is that the printed hue is the angle formed by a* and b* position on the black line at the requested saturation as given by the a* and b*. The actual saturation printed is on the gamut edge which in on the inner most magenta line.
The hue angle in degrees is: atan2(b*,a*)*180/pi