I think they mean that a quantum system entangled with another quantum system serving as a clock will create the appearance of classical physics including classical notions of time in the system when you observe it from a macro scale?

That way this theory tries to bridge the gap between quantum notions of spacetime and classical notions of space and time?

If that's not what it is then it's beyond me what they're trying to say.

In a very basic sense a "clock" is just a fixed oscillation. In CPUs, for instance, all your data is carried by bursts of electricity that you can think of like Morse code. Bits are delineated by the clock, which is one wire that lights up on a regular interval and does nothing else (the "clock signal"). Every other process uses that clock signal as a reference point to know when one piece of data ends and the next begins. Essentially the time between one clock signal and the next is one "frame" of CPU time and you'll usually have a few million or so of those every second.

So if we think of this in a physics sense instead of a computer science sense, a physics clock could be any particle or particle interaction that happens repeatedly on a regular schedule. It could even happen on an irregular schedule, there's no law saying the clock has to be consistent. I think it's probably on a regular schedule, but for all we know the pico-femto-Planck or whatever the basic unit of time ends up being defined as might have slight variance caused by who knows what. But the important idea to take away is that a "clock" in a fundamental sense is basically just any action that repeats. It could be or look like anything. Maybe time is tied to quantum foam fluctuations, or gravity in a general sense, or specifically the up quark doing something. I have no idea and I think this researcher probably doesn't either.