I don't know about how bike emissions controls are but I'd get one of those engines! DI 2 stroke is extremely nifty.
For cars at least I think the biggest challenge is knowing how much air is going through the cylinder. Since the exhaust and intake ports are blowing gases through simultaneously you either have really crap scavenging and a lot of exhaust gas leftover, or you don't know how much fresh air is blowing out the exhaust pipe and thus you don't know how much fuel to meter. Certainly there can be some temperature/pressure readings or something used to help the engine decide but they'll never be as accurate as having oxygen sensors giving feedback.
Of course, if you don't give a crap about NOx emissions this is a nonissue
