Gas(oline) engine has nothing to do with it. The AF mixture typically has some time to mix before reaching detonation conditions or being spark ignited. Looked back at some of their available info. They're injecting at TDC or essentially into a fully compressed vessel which wouldn't be without its challenges; achieving a somewhat homogeneous mixture being one of them. It would make for some interesting combustion dynamics at a minimum. Make me wonder if the associated combustion event takes a little longer to complete versus a CI engine that injects before TDC. Would be monster cool if someone with some specific insight would educate me here.

From a eyeball analysis, this would also seem to be detrimental for unburned hydrocarbon emissions. This is something two strokes already suck at. This will be a probably be a target for anti-aviation types (e.g. leaded fuel now) in the future if this PP gains market share.
In Direct Injection engines, the fuel is injected when it is time to combust, at very high pressure (29,000psi for common rail diesels) so atomization is instant. They don't rely on turbulence inside the cylinder to mix the fuel and air like a carburetor or throttle body injected engines. And in a diesel, there is always more air than fuel (until you get to critical altitude) since the air charge is always the same, only the amount of fuel varies, unlike a gas engine that wants the the mixture perfect every time. There just isn't an opportunity for early ignition, if there was, it would ignite early every time.

All the extra air is one of the emission issues diesels have historically had. All that extra air, plus the sulphur in diesel until recent regulator changes, made sulphur dioxide and nitrous oxide emissions high. The reduction of sulphur, plus the use of DEF to break down the nitrous dioxide before it exits the tailpipe have made significant improvements in emissions.

Unburned hydrocarbons happen in diesels when too much fuel is injected, then they start to smoke. When some idiot is 'rolling coal' after they take all the emission control off their squatted diesel pickup, all they are really doing is pouring fuel (and money) out the tailpipe.