Is this the datetime format they use onboard on the ISS or why is it being used in this webui?

This is the first time I come across this particular format, but also never near space-stuff so wouldn't surprise me if they use some specific format for some specific purpose.

Yes, using Day of Year for time GUIs and measurements is pretty common in spacecraft operations. Generally easier to do/plan operations for things like "we need to perform this maintenance activity every 5 days"

That's very common in ISS operation schedules - next spacewalk is on GMT xx next launch on GMT xx, etc

I expect it's easier and more useful to track days until event or days since event