That's what you'd think but it's a different thing.
They used a good example in the article there: tap a chunk of jello with your finger at a steady rate and you expect it to wobble in time with the taps, Discrete Time Crystals (DTC) exhibit a different period than the input alone should produce, so it exhibits behavior which isn't reversable in time like most things actually are. Dropping an egg and having it shatter is normal, and having a splattered egg reform and fly into the air is not normal.
At the subatomic scale though, you get things which happen one way and know that sooner or later you'll observe it happening the other way, your accelerator makes a particle split into a neutrino and muon, at some point you'll observe a muon and neutrino come together and produce that particle.
In a DTC you're getting behaviors which only take place one way in time, the crystal atoms are pulsed and begin to resonate, and then start to exhibit a different resonant period from the pulses used to initiate it, which isn't something you can reverse to generate a chain of atoms that stop resonating in that way and settle into a regular periodic cycle without using a completely different method, if it is even possible at all.
If you did set up something to produce the later form of a DTC and had it evolve to the prior form, it wouldn't work when reversed like everything else does in physics, hence it is a broken symmetry.
A crystal like in a gem doesn't have an arrangement you would expect, evenly spaced and randomly distributed elements, instead it has the property that certain directions and arrangements are favored, so it exhibits a broken rotational or translational symmetry from certain directions but not others. Rotating a series of events through time and not having them operate the same way is new.