Cable
The cable you're looking for is Type UF, or Underground Feeder cable.
It can be purchased at big orange, and big blue, by the foot. It's available in 6/2, 6/2 with ground, 6/3, and 6/3 with ground, and is rated for direct burial.
Attachment to Service
There is one temporary, and two permanent ways to supply power to a park trailer.
Temporary
Power-Supply Cord
You'll want to use a NEMA 14-50 receptacle, and 4 wire cord with NEMA 14-50 plug to connect the trailer to the service. The trailer's electrical grounding will be through the service plug, so only the distribution panel will have to be grounded.
Permanent
Mast Weatherhead
You can use four continuously insulated, color-coded feeder conductors strung from a mast to a weatherhead as a permanent feeder.
Raceway
A metal raceway, rigid nonmetallic conduit, or liquidtight flexible nonmetallic conduit, from the disconnecting means to a junction box on the underside of the trailer can serve as a pathway to run permanently attached feeders.
NEC
For reference, park trailers are covered in article 552 of the National Electrical Code.
My guess would be that because the fixture has a metal frame, the ballast is grounded via its contact with frame. If the frame were plastic, you would need to use the terminal on the ballast.
If you're converting it to hardwired, you should definitely connect the ground wire to the grounding screw.
You're also going to need to cut a hole if there's no punch-out available and make sure to use a cable clamp/strain relief suitable for using with romex.
Best Answer
Noting the irregularities in the way the strands are spiraled, that is certainly SE type cable, or "Service Entrance" cable. Service entrances (weatherhead to main panel) are run hot-hot-neutral with no ground, so naturally, SE cable provides exactly that. The bare wire is neutral, not ground.
Use of SE cable for ranges was legal in the 1970s, and as such, it is "grandfathered" today. It is neutral, not ground, which means your range has a 3-wire ungrounded connection, also legal in the 1970s.
While it's grandfathered to the inspector, it is not grandfathered to the reaper. 3-wire connections have a fatal flaw: in this setup, the chassis of the range is bonded to the neutral wire. If it has a simple and common contact problem, it energizes the chassis of the range with lethal voltage when the oven light is on (i.e. door is opened).
When fatalities happen this way, it is reported by the press as miswiring which is untrue: it was wired correctly but neutral had poor contact. Which happens.
The new doctrine is to provide a separate ground wire; or; fit GFCI protection at the breaker. Both of these solutions require removing the bad-news bonding strap inside the range that ties the chassis to neutral.
Merely removing the bad-news bonding strap is not enough; now the chassis will be energized by any ground fault (which grounding or GFCI would have detected).