What does the engine type have to do with sonic booms? The strength of a boom is based almost entirely on the shape and size of the craft making it (if we assume atmospheric conditions are a constant). I'm going to assume, for their sake, that the saucer shape is a "low boom" shape, but I really have no justification for that assumption. The whole phenomenon of sonic booms is that the air pressure in front of the aircraft cannot "get out of the way" fast enough, and thus compresses into what we call shock waves. Typically the way you lessen a boom is to disrupt those pressure waves via multiple surfaces, like canards (smaller wings, basically) in front of the main wing. That results in more but less powerful shock waves, and if you manipulate the placement properly they will somewhat disrupt each other. If you spread those waves out enough, the pressure differential as they hit you and other objects is significantly lessened (causing less noise). But the minimizing would only be done for certain speeds, because the shock wave becomes more acute the faster you go past the speed of sound. So they would likely design the aircraft to minimize the boom at cruising speed, meaning it will be bigger outside of that range. Because, contrary to what a lot of people believe from TV and movies, and from hearing one themselves, a sonic boom is constant for as long as the aircraft is supersonic. It does not only happen when they cross that Mach 1 threshold either. It is ongoing forever until you decelerate below that speed. You only hear it once because the wave has passed over you and continued following the plane. If you could somehow match the speed and position yourself exactly at the wave, it would be a continual effect (to be fair, no idea how it would sound if you could actually do that hypothetical, maybe matching speed would alter how it affects your eardrum).
I should also point out that distance clearly affects the strength of a sonic boom also. That's why the SR-71 could fly so fast at high altitudes and not alert people below with its boom. Get high enough and the shock waves dissipate before they hit the ground.
Now, getting back to the engine question, if you could somehow strap a tiny little engine onto that prototype and make it go supersonic, it would have a smaller boom than say the Concord because of its size. But would it be any quieter than a normal shaped drone that size? No clue, but just because its whole body is a "wing" doesn't automatically denote that. A B-2 is a flying wing, and if it goes supersonic it is still going to make a boom, and probably a fucking big one I'd guess. That saucer is literally just a rounded airfoil...which is what all supersonic aircraft use in some manner or another (even a dumpster with a rocket attached to it is an "airfoil" technically), and they can make huge fucking sonic booms. Scale that saucer up to the same size and I bet it big badabooms as well. Again, the type of engine literally has nothing to do with it. The only justification for that statement about "the right engines" I can think of is because someone erroneously thought that the engines are the main (or perhaps only) source of the boom. That's complete horseshit, because while the airflow inside (or outside in the exhaust) might be supersonic, that shock wave is tiny since it is based on the size of the fan/rotor blade, or the aperture of the exhaust. Sure, that shit is super loud on the ground standing next to it, but it quickly drops off with altitude/distance. But even assuming that somehow the aircraft is made to be virtually "boomless" except for the engine, what is the "right engine" to make something move at supersonic speeds without itself having supersonic flow somewhere in its mechanism? As far as I know, that's currently impossible. I mean, maybe they are talking about putting baffles on it or something, but I'm still completely in the dark as to what the "right engine" would entail. But hey, I guess if we just make wild claims on the internet, no one will question it!
I also realize it is Mashable, so getting triggered over it is similar to getting upset at something Vice says. But still!