based on your measurements of a spot of 75cm on a distance of 2m, the angle is indeed 21°.
in excel, =degrees(atan((75/2)/200)), this gives you the half angle. Multiply by 2 to get the full angle. However, with this measurement, it is unknown if this is measured at half maximum.
I checked the profile of the the spot and it seems more or less at half intensity when you just look at the entire bright spot.
1 reason that this is high compared to the spec, is because you use a different led compared to the specs. Another source of error could be rounded figures.
Also, it is possible (and most likely) that the ±4° is for a single lens and not for the entire lens assembly. I say this because the profile of the light gives a hotspot in the center (about 130 pixels wide which would correspond to about 29cm), then lowers significantly to about half intensity (which is the 75cm) and then slowly further down.
If I calculate the angle of the central hotspot, I actually do get 8.3° (full angle, so ±4.15°) which is close to the spec of Cutter. If you look in the datasheet linked on that page, you get however quite different numbers which are much closer to the measurements.
Having intensity changes in 3 steps is a bit unusual for a TIR optic so it seems to me that the optics are alligned perfectly parallel while you would get a better spot at a certain distance if you would change the angle of the outer optics (including the led) to allign the spot with the center optic.
You can probably verify this by blocking al but 1 optic of the assembly.
anyway, never thrust angles given by others than the manufacturer and always check the datasheet. Given the datasheet numbers and the fact that the OP wants to use XPG's, the optic from polymer optics seems like a reasonably good one.
Johan