The ideas of who did what are fragmented but for gameplay capcom has done most. For example the Vergil vs Dante was taken from dmc3. Kat is their own idea. The angel thing is by NT, i read Tameem said it to make NTDante more special.
So, why did Ninja Theory include the half-angel part?
I asked Ninja Theory’s Creative Director, Tameem Antoniades, this very question at E3. Antoniades told me that Capcom had rules about which parts of the Devil May Cry canon Ninja Theory could change in their reboot.
For their part, Ninja Theory wanted Dante to be something special, like nobody else on Earth—almost like a secret weapon against the demons. Because the world is run by demons who throw their weight around, Dante being an angel makes him special.