The video above is surely just the tip of the iceberg, the small part of development that they feel they don't need to keep secret.
Ever-so-slightly-educated guesswork follows. (Purely mine.)
They're running on the verge of detonation, but still keeping rate of combustion finite so that it is a progressive almost-self-ignition and not a simultaneous ignition everywhere in the combustion chamber.
They're not relying on in-cylinder charge motion as much as conventional production engines do - they're getting the speed of combustion via the plasma-jet ignition and the almost-but-not-quite detonation. The flat-pancake shape of a F1 cylinder (due to the extreme bore/stroke ratio) doesn't lend itself to tumble charge motion that is typical of production 4-valve-per-cylinder engines.
Completing combustion very quickly, in a small number of crank degrees and while the compression is high, cuts down on the time available for heat transfer to the pistons.
The big bumpy cams necessary for high-RPM peak power leads to lower dynamic compression ratio at lower revs, so detonation at lower revs probably isn't as much of a problem - the effective compression ratio will be lower because the volumetric efficiency is lower. These engines will not have friendly, smooth, daily-driver-suitable torque curves.
Running high lambda keeps peak combustion temperature down.
They're probably doing some in-cylinder stratified-charge trickery to keep the mixture next to the piston as high lambda (lean) as possible to act as an insulating layer.
High lambda (high dilution) plus completing combustion very quickly so that the burned charge is more fully expanded, cuts down on exhaust-gas temperature.
Cutting down on heat transfer to the pistons (and head) is an important bit of improving engine efficiency.
A nuisance with Achates is that you can't put the injector and spark plug in the center of the chamber, because there's a piston there instead of a cylinder head. Not saying it can't be done, but it would need a re-think of the combustion process.