I race rotaries. yes, initial start up can be a bear.
You say it has 80PSI. That's a bit light, but, not surprising. Proper rotary comp tests are done with a Mazda part, a strip recorder. It's essential for determining the condition of each 'chamber", and you can determine easily what problem a rotary might have with one. You can test without one, by using a typical tester, but it must be one that doesn't hold the reading. Watch the pattern, and make sure each pulse is equal. One or two that are low indicate a mechanical problem. It's critical to get he side seals and apex and corner seals filed and sized within thousands and square. Failure to do so will show in uneven compression.

OK, assuming it's built correctly internally*, and it's a Mazda, lets concentrate on the basics.

Timing. Can you (your friend) SEE a strong spark? Obviously, a good starter and strong battery and good coil, and plugs (fresh, and proper temp range) and wires are key. To ensure the crank markings are synchronized properly, with the plugs out insert a rounded tip dowel in the front lower plug hole. Rotate the engine by hand in the firing direction. It should push the dowel out as you approach the timing marks, and be essentially as far out as it can be when the timing marks are lined up. Now, align the distributor device so that it points to the proper rotor feeding that plug. (assuming it's a rotor driven spark). (or assure the timing and wiring of whatever system you have)
Note. The second, or higher plug adds little to power, and is mainly there to clean emissions. It helps power but it's not critical, the engine will run without it. The Upper plugs are called "Trailing" the lower "leading". I remember that by thinking Leading =Lower, L=L, and T railing =Top, T=T. #1 rotor is the front of the engine.

Fuel: I have a carb, so it's just a matter of sucking fuel in on the vacuum of rotation. If yours is injected, make sure the timing is synced properly, the fuel pressure is appropriate, and the injectors aren't frozen, etc..

Cranking a reluctant to start engine can wash the walls free of oil, killing compression. A bit of oil into the intake runners can restore compression. Without compression, the thing will never start. ATF is a popular choice for this as well.

Slow cranking and cold rotaries have a difficult time starting on normal gas. Ether can kick them off much more easily. Give that a shot.

If it starts on ether, but won't remain running, it's likely a fuel issue. Too much, or too little. Cold rotaries can need significant 'choke' to start. (My race car has no choke, so 40 degree morning starts are a bear, and much pumping is needed. I do 10 accelerator pedal pumps, turning the engine over on #7-10, then switch ignition on). Check the plugs and see if they are wet, oiled or dry. If wet, obviously it's flooding.
Once the thing starts, be prepared to kill mosquitos for miles. The neighbors will be curious, or will call the cops, LOL. Vaseline is used liberally in assembly, and there's always extra fuel, and oil in the thing. It makes a smoke show. Further, it takes some rotations for the oil seals and side seals to set. So it might smoke for a half hour.
Make SURE it is cooling properly. And Make SURE the apex seals are being fed the proper lubrication, either from the metering pump, or premix, Dry apex seals will overheat, and warp, (in 30 seconds or less at speed!)and the thing will be a bear to restart, and never run right again. Proper lubrication and cooling are critical to the power and longevity or these engines. make SURE it builds good oil pressure upon start up, and temps never exceed 220 water, and about 280 oil.

Since this is an aircraft engine, there are duplicate components, and it goes without saying that those need to be tested and renewed as well.

*As mentioned, if he rebuilt the existing components and didn't start part swapping, it should assemble properly. Its a pretty easy, but meticulous process. The trickiest part is in the front cover area, making sure the thrust bearing is properly assembled and the oil pump drive is in place. If his compression is a pattern like "hi-hi-low-hi-hi-low, etc, he has a side seal issue on that rotor. if it's hi-low-low-hi-low-low, he has an apex seal issue on that rotor. If it's hi-hi-hi, then that rotor is sound. Cranking the engine with no plugs in it will produce a pretty loud whoosh whoosh whoosh sound, and be accompanied by a lot of mist and fuel/oil being ejected from the plug holes. It's a good way to clean out the housings if flooding is suspected.

Good luck!

(Also, I too am surprised this is coming up on an aircraft engine. I thought the FAA had very strict rules regarding FAA approved rebuilders and were very strict about when to rebuild engines and how hours were logged. (Which drives up the ownership costs of airplanes, of course. I'll assume this plane falls under some more liberal homebuilt rules, or something similar)

Thanks, that is huge help! I will report back soon.

and yes it's going in a homebuilt/LSA/experimental class aircraft, so basically no rules apply.. lol ( and no, i'm not going to fly in it.. !! )

Be sure and introduce your friend to Dynon Avionics.