How do wireless subwoofers do this?

Subwoofer DSP room correction does not implement a crossover. A preamp with bass management will implement a crossover.

A crossover is a combination of 2 filters.  Low pass and high pass.

A subwoofer's input can certainly implement the low pass. The high pass function is the main speaker's natural roll off.

So, it is possible to implement this limited filtering in the subwoofer alone.

On a related note, anyone has direct experience how these 'wireless" subwoofers sound as compared to the 'wired' models? I assume the importance of the impedance matching between the preamp output and the plate amplifier still applies. The concept can definitely address some general room placement issues associated with wiring and cabling.    

I have 2 of my 5 subs connected wirelessly. They don't sound any different than they did when I was using cables.

A download of the Syzygy application will give you a clear description of their DSP design. The 120 or 80Hz crossover settings your referring to sound like a surround receivers LF/Sub bass management settings.

If your electronics offer a separate pair of left and right RCA/line outputs they're what you'd use to connect to a wireless transmitter or directly to the subwoofer. 

Many powered subwoofers provide crossover adjustment as do a few preamplifiers. Since DSP can vary greatly crossover adjustment can range from a simple variable dial to a wide range of multi frequency bands of analog filters or digital parameters. 

This level of detailed crossover adjustment has been included on a few powered subwoofers and in the aftermarket for over a decade. To the best of my knowledge reviewers have only commented on the ease and improvement of a products auto equalization but little or nothing on the potential of a products manual adjustments. Its not a widely used tool but the effort and results can be quite satisfying.

Thanks to erik_squires whose been commenting on his methods.  

Both my subs are wireless but I have never bothered to try them wired so cannot compare.

However I went wireless for a different reason to most I am sure.
With my old wired sub I was getting some ground loop hum I could not eliminate.
The first wireless sub cured that and even though I have changed main equipment since which may have also fixed the ground loop hum I have never bothered to try wired again.

Besides as noted it does make placement and cable runs much less of a problem!