You are right, Tobias. There is only one dhammatā, which is dhammaniyāmatā. The sutta you referenced explains that.
It seems that the five “five dhammatā” was made up by someone in a commentary. It could be Visuddhimagga, but I am not sure.
– If a key principle is not referenced in the Tipitaka, it is safe to assume that it was made up by someone at a later time.
I had come across a discourse by Waharaka Thero which addresses this issue about the “five dhammatā“. For the benefit of those who can understand the Sinhala language here is the link:
“කර්මය, නියාම ධර්ම”
– Explanation within the first 30 minutes.