That does indeed describe a properly engineered 50 amp device.
It is normal for appliances to use slightly lighter gauge wire than would be used in building wiring. You can observe that inside electric ranges, dryers, and water heaters, where you will see the 10 or 8 gauge incoming supply wires to a terminal and then 12 or 14 gauge wire going from the terminal block off to the components.
Because the wire is inside an enclosed box, and is not tightly bundled or surrounded by thermal insulating materials, its elevated temperature will not cause any danger. It will run a little warm at peak current, but be far below "hot". The same is not acceptable inside dwelling walls were it will be in contact with wood, fiberglass, cellulose insulation, etc.
As for standards, I have determined this is beyond the scope of the NEC and falls into the domain of the National Fire Protection Association (NFPA) standards. That seems to cost $$ to view.
If you want this to look decent, and be safe. You want to have something like this:
Circuit Protection
This setup assumes that the generator provides overcurrent, short-circuit, overload, and ground-fault protection. Likely via a circuit breaker, and a GFCI receptacle. If this is not the case, you'll want to provide that protection within your wiring.
If the generator output does not have short-circuit, overcurrent, and overload protection, you'll want to install a circuit breaker somewhere (likely between the inlet and the receptacle). If the generator does not provide ground-fault protection, you'll want to have that somewhere as well (likely via GFCI receptacle, or GFCI circuit breaker).
Shock Hazard Protection
You'll notice in the above diagram, that an inlet is used, and that the female end of the gen. cord plugs into the inlet. To understand why this is important, let's take this example.
The power goes out. You go out and start up the generator. You plug one end of a double male ended cord into the generator, and drag the other end over to the "input receptacle". As you do so, you touch the exposed prongs at the end of the cord. ZAP! You dead.
If the generator does not accept a male plug connection, you'll want to make up a double female cord. That way you'll plug a female end into the generator, and a female end into the inlet. You don't ever want to have exposed energized parts, as they are a serious shock hazard.
Sizing
Make sure all wiring and devices are sized properly. If you're working with a 20 ampere 125 volt output from the generator. That would mean 20 ampere devices, and at least 12 AWG copper wires.
Grounding
As this setup is basically an extension cord, there's no need to bond it to the electrical system of the house. The neutral-ground bond on the generator should be left in place.
NEC 702.11 says that the generator has to be grounded to a grounding electrode in accordance with 250.30.
Signage
According to NEC 702.7(C), there should sign near the inlet that reads:
WARNING:
FOR CONNECTION OF A SEPARATELY DERIVED (BONDED NEUTRAL) SYSTEM ONLY
Best Answer
Take that range cord back and get the correct cord for the job
50A generator inlet boxes, as well as many generators with 50A outputs, do not use anything resembling the NEMA 14-50 that is certainly on the end of your range cord. Instead, they use locking type connectors; unfortunately, there is no such thing as a NEMA L14-50, so California had to step in and set their own standard for this, the CS6365C/CS6375 family. Furthermore, the type SRD cordage that is used for range cords is not rated for wet locations or hard/extra-hard usage, making it utterly unsuitable for use outdoors, even if your generator uses a NEMA 14-50R for its 50A receptacle.
As a result, you're better off taking all your stuff back and getting the proper generator cord for your generator. This will have a CS6364C cord-connector on it to mate with what is almost certainly a CS6375 inlet on the generator inlet box, and be made from extra-hard usage, wet-rated cordage such as type SOOW, with a 6/4 wire configuration, and either a NEMA 14-50P or a CS6365C plug on the other end, depending on what your generator uses.