We're beating a dead horse: but, to answer the original question, let's go to the information given, the code requirement, and wire ampacity.
The information given is it's a welder with 25% duty cycle, and manufacturer recommendation of 50 amp breaker.
First way is to assume manufacturer has sized max breaker to correspond with actual machine max current.
From ampacity chart below, for NM-B cable, 50 amps requires #6 copper wire. So, from a strict non/exception standpoint, you would install a 50 amp breaker, and 6 ga copper NM-B. If you installed conduit, and 90 degree wire, you could go to 8 ga copper.
However, the NEC Article 630.11 allows derating conductors for welding circuits, based on duty cycle. for 25% duty cycle (interpolate between 20% and 30% duty cycle), a 50% derating is allowed. So, the 50 amp circuit could be derated to 25 amp. This would allow 10 ga NM-B to be used, or 14 ga 90 degree THHN in conduit. The breaker can remain the same as the un-derated value, or 50 amps. In fact, the code will allow the breaker to be upsized one size
if nuisance trips occur. However, the code also limits breaker size to 200% of derated wire ampacity. So, the 50 amp max breaker would be required. Of course, a smaller breaker could be used, but could result in nuisance tripping.
Now, the question comes up of what is the real max current draw of the welder? It is likely less than the breaker recommendation, as the manufacturer probably took into account some of the derating in code in their recommendation. If it is actually less than the manufacturers breaker recommendation of 50 amps, then the calculations would need to be run again with the real current.
So, the OP's decision to go with 8 ga NM-B wire, is code compliant and slightly conservative for a welder circuit that could be derated to 10 ga.
Given the constraints that sberry has put on his installation recommendation, he could use 14 ga THHN in conduit, and meet the letter of the code for a derated welder circuit. However, the 30 amp breaker he recommends might be subject to nuisance trips, and could be upsized to 40 or 50 to eliminate nuisance trips and still meet code.