There is nothing, in either code, nor any standard or trade practice that I've encountered, that would in any way infer that it was, in any way, wrong to use a round orange cord, rather than the flat grey one you usually see attached to a dryer.
Nor is there any requirement that the plug be a molded-on angle plug, rather than a big fat round one.
Finally, it is nowhere written that the 'manufacturer' of anything must be someone other than the final user.

Let's look at the cord in question. One might be able to infer a code requirement that it be 'hard use' (SJ) or 'extra hard use' (S) type. It has to be rated for at least 250 volts, and be of sufficient size for the current drawn by the appliance. The plug SHOULD be appropriate to the receptacle, and it's nice if they conform to NEMA patterns. Yet, there are perfectly acceptable plugs out there that do not match NEMA patterns.

The code may limit the length of the cord .... this is one area where I often disagree with the NEC, and might rely upon the NEC's general provision that virtually anything may be waived by the AHJ. For example, placing the receptacle where it can be easily reached, or having a cord long enough to allow for easy access to the receptacle when you pull the appliance out, can often mean using a cord longer than the code allows. I see some 'wiggle room' there. I'd rather see a seven foot cord on an appliance, than a 3 ft cord combined with a 25 ft extension cord!

Then there is the more important, nay, most important part: how is the cord attached to the appliance. If you pull on the cord, is that tug felt where the conductors are connected to their terminals? I'd look for a proper strain relieving fitting, one that relieved such forces, as well as protected the cord from sharp edges as it leaves the appliance.

Finally, there is the 'obvious' to consider: Is the appliance part of the deal? It simply would not do to raise a fuss over the dryer ... when the dryer has a future in the movers' van