Most likely your engine also needs a computer, which implies an electrical system.
Old diesel clunkers not really, at least if you don't care about emissions control. Fuel injection / exhaust valve control is purely mechanical, all they need electricity for is the engine starter and, depending on age, the cooling fan.
Modern engines, on the other hand, these can be really hard to run on their own outside of a car, at least from hearsay - I only have had experience with an 1994 VW T4 van.
If you get an old enough diesel engine or can do the mod yourself you don't even need an electric starter. The first diesel engine I worked on used a gasoline engine as a "pony motor" to spin the diesel engine flywheel enough to generate the compression needed to start the diesel engine. From memory (probably wrong haha) you cranked the gasoline engine and brought it up to high rpm and then you started the diesel engine using a lever that gradually engaged the diesel engine flywheel bringing it up to operating speed. Once the diesel engine was running you backed off the lever and killed the gasoline engine.
An obvious disadvantage would be the necessity to maintain stocks of two fuel types. Other than that it is a near fool-proof way to handle cranking a diesel engine. The electric starter is replaced by the gasoline engine and flywheel linkage. You effectively roll-start the diesel using the gasoline engine.
Wouldn’t a starter motor running off a battery charged by the very generator you are running just be an all around better solution? You can run some modern starter motors off a tiny 12x8 in AGM.
I have to add a frequency meter on the generator so that I can make sure I get some clean power and a power conditioner to smooth all the wrinkles so my electronics inside the house won't be damaged. Then I need to have an electrician add the subpanel and manual or automatic power transfer switch but for the price I paid it is a bargain over the usual generator packages available.
https://youtu.be/AL0ls_UpT8w?t=361
The whole video is worth a watch, but I linked directly to the timestamp where he begins to explain how the engines are started with a petrol starter. To power a foghorn. Amazing stuff.
Here is a video of a guy cranking a Caterpillar D2 like we had to crank our D4 back in the day. [0]
When I started working with that small family-owned company I had no real experience with mechanical things other than my own pickup truck. When I finally moved on from them a couple years later I could maintain, tear down, and rebuild gasoline and diesel engines, compressors, hydraulics, air brakes, etc. We did all of that ourselves in addition to the real jobs of pipeline maintenance and repair and oil spill cleanup. I don't remember all the times I spent laying on the dirt floor of the "shop" there in central Texas and cursing all the oily sand and crap that fell in our eyes and faces as we tried to fix things after the day's work was done. Luckily beer-thirty was a cherished event that came with hang-down (summer sausage), cheddar cheese chunks, fresh onion slices, cold milk and saltine crackers. We finished most days in the domino shack trying to avenge the previous days' losses. Good times indeed.
Chances are you won't be running 4 YouTuber editing machines, 2 pots cooking on IH stoves, 2 air conditioners and a USB-PD laptop charger all drawing full amount inside the living quarter on a sailboat. That's before counting in 6x 12V/200Ah = 14.4kWh battery system which safely doubles, possibly quadruple instantaneous draw.
Average household usage in US is 20-40kWh/day... not sure where does 13kW figure fits in that picture.