They're not unitless, they're dimensionless, see https://math.stackexchange.com/questions/803955/why-radian-i.... I think the author made a mistake.
https://en.wikipedia.org/wiki/Radian
> the SI unit for measuring angles
> defined in the SI as being a dimensionless value
Relevant wikipedia article: https://en.wikipedia.org/wiki/Dimensionless_quantity
Radians and degrees are both ratios where the units cancel out - ie. m/m. The point that is made is that adding degrees to radians without any conversions is technically fine from a dimensional analysis perspective, but it's often a bug in programming that we might want to prevent.
You can define 1 meter as ratio between the measured length and a known length. Both of these have the same units so they cancel out, just like with degrees/radians.
The only difference is that full circle is a little less arbitrary than Earth circumference.
How are they unitless if you add ° behind one and "radian" behind the other?