At full load, you're not running in lean-burn mode, and with direct injection, there's no direct loss of fuel to the exhaust ports. At full load, one would expect that the emissions wouldn't be too different from a 4-stroke engine. All the stuff still has to go through a catalyst to clean it up.
And on that point ... 4-stroke spark-ignition engines usually intentionally run somewhat rich at full load to protect pistons and exhaust valves. The standard automotive EPA drive cycle does not include any full load operation at all, and it's possible to arrange for the more aggressive US06 to not include full load operation, either. Some underpowered vehicles may need intermittent full throttle for that one, but you can game that by operating stoichiometric for a certain time delay then going rich to protect engine components. This isn't really much of an issue since existing 4-stroke engines have a problem with full load operation anyway. If anything, the 2-stroke operation will allow a bit of air out the exhaust ports to allow overall lambda=1 even though in-cylinder lambda can be slightly rich if it's necessary to protect the piston.
One other thing that two-strokes have trouble with, is that the ports in the cylinder wall inherently let some lubricating oil out the exhaust, even on engines without crankcase scavenging. Don't know how they're handling that - this is a trickier problem than full load.