here are my 2 cents for this project:
From the picture you provided, it seems like the generator has a on / off switch
If you carefully disassemble this switch, and plug the 2 wires in a normal relais, you should easily be able to control this switch with a Arduino / Raspberry PI.
Of course there is a starting pull line on the generator, and this is the main problem with this build!
If this is just a failsafe to start the engine if, for example, you have gasoline in your cylinder, it should not be much of a problem.
But if you have to pull this line to actually start the engine every time you want to use it, then you'd have to forget about it. In the specifications it says
"start type: recoil"
so that would mean to me you'd have to pull the starting line each time you want to power on the generator! While there are some "zugmotor" (dunno english word, sry) like this one here
, it would (in this little format ) hardly provide enough power to start the engine... Although there are special "zugmotoren" that can provide enough power to quickly open a door, for example. I believe these work with kind of a spring in some sort, that is already under much tractive force to begin with, and would only need just a little push to activate. But better forget it, too expensive, too specific, too overkill for a simple power generator.
Maybe you could build a starter motor from a car into this, but then you would again need a battery just to start your engine...
Better: Use batteries in the first place, and a voltage transformator to whatever you need (I think car batteries provide 24V per default, but maybe this is only true for germany). If the system works normally, you could charge the batteries, and if power drops, you switch to the battery (while having kind of a big condensator or something to safe you until the battery kicks in)
EDIT: So now you changed the generator in the link. This one looks awesome, I want to have one like that, too! And if you watch, it is controllable by remote, which means you could go for a 433MHZ sender wired to the raspberry, no need for further wiring. Good luck with your plan!