Funny that they go to a dictionary definition - that's because if they read the definition from the same code that defines a money transmitter, their argument falls apart:
"Money Transmitter":
https://www.ecfr.gov/current/title-31/subtitle-B/chapter-X/part-1010/subpart-A/section-1010.100#p-1010.100(ff)(5)
"Transmittal of funds":
https://www.ecfr.gov/current/title-31/part-1010/section-1010.100#p-1010.100(ddd)
"Funds transfer":
https://www.ecfr.gov/current/title-31/part-1010/section-1010.100#p-1010.100(w)
These regulations clearly are about financial institutions accepting orders to pay (negotiable instruments) and paying a third party on someone else's behalf.