For this kind of project, given the stakes involved (e.g. a defendant's freedom), why would you want to use the brand-new framework-of-the-month that the cool kids are using?
The actual codebase itself may be pretty old so WebForms isn't a surprise - the SLN file indicates it was saved with Visual Studio 2010 (https://github.com/propublica/nyc-dna-software/blob/338a1b86...).