You'll note they don't actually specify any asymmetric quantum-resistant algorithms. I'd guess if they did, NTRU or a derivative would be one they'd consider first: Security Innovation were trying to sell them that at about the same time Certicom were pushing elliptic curves. (I'm not as convinced about ideal lattices, but that's an artifact of my not being as familiar with the field.)

Pre-shared keys, as they suggest there, have no forward secrecy - which makes them great for those who really like stealing, say, IPsec keys… like the NSA. It may work with the kind of old military key infrastructure they and GCHQ have, that regularly distributes random keys from centralised, organisationally-trusted sources on specialised hardware; it is a terrible recommendation for civilians.

Interesting that they're still married to P-384 (probably the most annoying curve to implement correctly). Properly-implemented Ed448-Goldilocks is safer, and that's what CFRG are going with for the "paranoid" level.