I actually recognize the drone body that Matternet is using there, it's a monocoque molded carbon fiber + fiberglass body from a manufacturer in China, where it's sold as an agricultural spraying drone.

Rapid descent sensors don't necessarily need to be pressure based at all. While in controlled flight there is a limitation (as governed by flight controller and ESCs) for how rapidly a quad, hex or octo can descend. Accelerometer data can be used to trigger a parachute and/or airbag system. A multiply-redundant array of small accelerometers that can detect freefall is very tiny and light weight.

Most higher end flight controllers have double or triple accelerometers onboard.