In his video, Anton Petrov is referring to this paper. The main idea of the paper is not new. In some situations, rotation governed by the triaxial and tidal torques is unstable -- and periods of sporadic rotation and even wobble are possible.
["The triaxial torque" is a jargon term for "the torque caused by the permanent dynamical triaxiality".]
One of the mechanisms causing instability and chaos will be easy to understand if we recall that a triaxial body librates in longitude around any spin-orbit state, not only about the synchronous one. E.g. Mercury is librating about the 3:2 spin state. Now, if the dynamical triaxiality is sufficiently large, the magnitudes of longitudinal libration about different spin-orbit states may overlap -- and that will result in a stochastic walk over spin states. This is just one easy-to-visualise mechanism leading to chaotic rotation. Rotation may also become unstable w.r.t. latitudinal libration -- which will cause wobble and perhaps even flips.
Whether a rotator falls within a chaotic zone -- is a delicate problem requiring accurate modeling. In Ibid., a mathematical inaccuracy is easily discernable. Their equation (4) is derived within the CTL (constant time lag) tidal model, i.e., under the assumption that the quadrupole Love number divided by the tidal quality factor, $k_2/Q$, scales linearly in the forcing frequency. Right after that, the authors switch to the CPL (constant phase lag) tidal model, one assuming $k_2/Q =$ const. Without an accurate check based on a right expression for the tidal torque, it is impossible to say if this oversight is fatal.
Another problem with this paper is that it does not say a word on the employed values of the dynamical triaxiality. Also, to calculate the tidal torques acting on the TRAPPIST-1 planets, the authors are using a model developed for TRAPPIST-1e. The model endows the planet with both an atmosphere and an ocean. I am not sure if this model is applicable to planet e (or to b or to d), because it ignores these planets' violent past. Calculation shows that during their initial tidal spin-down these planets were captured into a 3:2 or higher spin-orbit resonance, like Mercury. Being very close to the star, they then underwent a thermal runaway caused by tidal overheating. This made them hot and plastic, so their rheology changed, and for this reason they slipped out of the higher resonance and continued their slow-down towards synchronism. I am not sure if after this episode they can sustain a water ocean. Most volatiles are probably gone.
Generally, a bona fide model of stochastic rotation must include calculation of the tidal dissipation rate. When a body gets captured in a nonsynchronous spin state, the tidal bulge is running around the circumference, and the heating rate increases by orders of magnitude. This changes the rheology, making the body more viscous. As a result of this, the quality factor is reduced greatly, and the triaxiality is no longer sustained -- which sets a limit on the duration of such periods.
To conclude, while the mathematical model needs some attention (and, probably needs to be redone completely), and while its applicability to TRAPPIST-1 inner planets is discussable, the central idea is correct. Sporadic rotation is possible, at least in principle.