Oh, wow. There's a ton of info around on this, been around for a number of years. I've been following the development for a while now. I forget who the lead researcher is on the project, but he's a reasonable guy and actually answered the e-mails from an overenthusiastic hobbyist technological tire-kicker a few years back!
Reactivity-Controlled-Compression-Ignition is what the RCCI stands for, if you didn't want to watch the video. The gist of it is, they combine both a relatively high octane (low reactivity) and a relatively high cetane (high reactivity) fuel to produce a mixture that ignites with the correct delay, given the current running parameters inside the engine. Early versions used two separate fuel injection systems - one direct for the high reactivity fuel, and one port for the low reactivity fuel. The next step was coaxial direct injection for the fuels.The latest is a single "correct reactivity" fuel, basically switching over to HCCI entirely. IIRC about 75 octane was the choice fuel. Some really impressive results, for sure!
From a combustion dynamics standpoint, the initial lean homogenous low-reactivity fuel/air mixture gets heated up during the first part of the compression stroke. A shot of high-reactivity fuel is fired in and starts to mix and react, creating some interesting mixtures. Then one or more later injections provide the bulk fuel and "kick things off", not sure in what order. By varying the mix of which fuel is injected, how much, and when, they can vary the reactivity of the mixture in the cylinder as it is being compressed in the cylinder, with the goal of having it "go off" at the appropriate point before top dead center for best efficiency. They've got to be careful to keep BMEP from being too excessive, though - basically you can make these things chew themselves to bits with detonation if you get the timing wrong and/or get the reaction rate too high. I think that last little spray of high-reactivity fuel gives the "kernel" to start the flame front moving swiftly through the all ready to go mixture, without over-compressing a bit in a corner and making it go bang, causing knock.
It's unfortunately a bit more complicated than just strapping on a separate port fuel injection system to an existing diesel engine - you need to have full control over both systems and be able to vary the injection timing and pulse-width for multiple injections from both systems.
Do note that this is not entirely unlike the various "fumigation" systems that are available for diesel engines, using CNG (pilot gas ignition - common for burning "sour gas" from landfills), LPG (common for power boosts on trucks), and methanol/water injection (common for tractor pulling). It's just quite a bit more sophisticated on the programming end.
I have actually found a few papers, IIRC from India, detailing adding a carburetor to a mechanical diesel engine and basically having the engine suck in varying A/F ratios of gasoline (all quite lean). Might even have been an IDI engine. It ran, and I don't recall them saying anything about blowing up an engine.
That said, it probably would not be beyond a dedicated tinkerer to set up a system to work really well in a relatively narrow RPM/power band, ideal for pulse/glide or hybrid setups. Their most impressive thermal efficiency in the dual-injection system used direct injected E85 with port injected biodiesel.
Poke around on the web using RCCI as your initial search string, and you'll eventually unearth enough papers so you get actual injection timing information and the test engine being used. Someone skilled in the art (dedicated tinkerer) could extrapolate from those to get a given engine running in the sweet spot, most likely.
The killer preventing this particular technology from being attractive to take to market so far is the dual (gotta use both diesel and gas) or "different from current" (where do you buy 75 octane? Mixing diesel and gas in one tank is dangerous, best to get a commercially prepared fuel with the right vapor pressures, etc.) fuel requirements to make it work. The dual-fuel version could probably be commercialized as a "diesel primary" type, with backup operation running on diesel alone at reduced power and efficiency, but it's a lot of extra fuel injection and plumbing hardware and an extra gas flap, etc. for a driving market (USA) that already shuns putting E85 into flex-fuel vehicles and rarely plugs in the various PHEV's.
The points that MetroMPG brings up about Brazil's little gasoline tank for cold starts and the "but people seem to use DEF ok" for modern diesels point to a way forward, but this system requires quite a bit more of the "other fuel" than either of those approaches. You don't just occasionally fill up the little tank with a gallon jug of X. You fill two tanks about half the size of your current fuel tank (or a bit smaller) every time you fill up. Two hoses, two gas flaps, two knobs, two card swipes, etc.
A new low-octane fuel seems a better bet. Maybe E85 and diesel can mix well enough without making explosive fuel vapors that a blender pump could do it, though I bet you'd want a dedicated hose! Getting a hose-full of 75 octane mix in your small "obligate E85" converted motorcycle could really ruin your day...