This is a nice practical technique for open quantum systems with relatively low entanglement. The introduction lays out exactly what regime they're aiming at:
1. Affordable (laptop scale)
2. Captures "sufficient" quantum effects (low entanglement regime; you accurately can't simulate a quantum computer with this)
3. Straightforward to implement.
From a cursory glance, it does all three. I'm slightly surprised that TWA hasn't been applied to open systems extensively before, but it was always a relatively obscure technique. I'm guessing this should be quite useful in practice for e.g. AMO and cavity systems with relatively large dissipation terms that prevent entanglement build up. However, I'd guess this wouldn't do very well near phase transitions. All-in-all, a nice new technique for a regime that didn't have too many options.