Is there any standard encoding that has evolved on the digital encoding side? Just as 4 to 20 mA is de facto standard on the analog side especially in process control?
Not really. Well, I²C is pretty standard for a lot of small sensors, SPI is even simpler, but needs a chip select line for each sensor if you connect multiple to one bus master; 1Wire is popular, too, and is pretty similar to what's used here.
For high-rate ADCs and sensors including those, JEDEC specifies standards like JESD204 – but these are completely different kinds of beasts.
You've got to realize that hardware components are built for a purpose.
I guess the purpose of the pressure sensor in the original question was to be a cheap, yet high-resolution sensor for usage with a microcontroller. The protocol used doesn't need high-quality oscillators or clock-keeping on either sides, it's easy to generate and decode, it's not terribly high-speed but easy to drive, and needs but one line for communication.
If you'd built a sensor that gave 1 million readings per second instead of that sensor's 0.000040 million readings per second, the protocol would be impractical, and you'd use something else.
In any case, using an analog current feels a bit arcane to me – I like the fact that current-based communication is less prone to errors, but if you'd communicated using digitized values, for example over a digital current loop system, you'd get the same error-safety for far less power consumption, and at a much lower system cost. I consider analog 4-20mA a "legacy thing", with a very specific usage scenario: Sensor that directly integrates into process control devices that only accept 4-20mA signals. For everything else, the "standard" is suboptimal.
So I wonder, in applications where rapid change is crucial, say airplane control, avionics etc. what sort of protocols have become the convention? Do they use 4 to 20 mA or PWM or dedicated buses?
I don't know about avionics – but in cars, using dedicated digital buses like CAN is the norm, and they can use very resilient physical layers at relatively high rates.