The bullet points seem pretty clear, there should be little doubt about them.
Your concern about the cable description is justified. While I think most people, if motivated, could figure it out and buy a proper cable, in this situation going for the lowest common denominator is appropriate.
If this were my marina, I would list the NEC code so there would be no doubt. Then I would identify acceptable brands, like Marinco, SmartPlug, etc.
To be even clearer, add a plain language description, such as:
The only acceptable power cords are those cords in good repair with sealed plugs. Cables must be appropriately sized for the current, i.e. a minimum of 10 gauge wire for 30 amp service, 8 (?) gauge for 50 amp. The cable cover must free of any damage such as cuts, cracks, or chafe. Connectors and cables shall be free of corrosion and shall not show evidence of overheating, scorching, or burning. Homemade or DIY cables are not acceptable. Commercially produced cables that have been modified or repaired by adding or changing connectors, splicing, or shortening are not acceptable. Adapters of any type may not be used. The management has the sole right to determine the condition of the power cable and whether it is acceptable for use in the marina.
Boat owners are encouraged to use SmartPlug cables and to add an ELCI and GFCI to their AC system.