That's a neat idea! I initially thought he was going to use an Arduino to control the whole heater haha, guess he's just using it to convert the pulses from the diaphragm pump leads to PWM for the motor, essentially.
However, I don't know if a peristaltic pump is the best solution for this. First off they're not particularly reliable. I work with Stratasys 3D printers that use peristaltic pumps pretty extensively as first-stage pumps, and they break all the time. Good news is they're cheap and easy to replace. Don't know if I want to be crawling under my van in January at 3AM to replace a pump though lol.
Which leads to my second concern: Most vans have their pumps mounted externally, so the tubing the pump compresses would be subject to the cold, probably not great for it.
And three: flow rate can be difficult to accurately control. Especially at the low flow rate needed for a diesel heater. If you look at his pump towards the end of the video, and think about the internals of the pump, at the rate shown, it will rise in pressure for about 5 seconds, then drop to no pressure for like a full second, maybe even a slight negative pressure (from the pump arm disengaging the tubing, before the fluid from the next arm moves up to fill the void.
Now I'm admittedly naive about the internals of diesel heaters, but I'm pretty sure there's nothing in between the external pump and the combustion chamber nozzle to regulate the pressure, so a full lose of pressure from the output of the pump for >1 sec could cause flame failure.
Don't get me wrong, I'd love to get rid of the diaphragm pump, I also hate the clicking haha. Just think we'd need something with more precise flow rate control at that low a level.