They've been sounding this progggy for a while. It's Don Airey's prog roots (he played in Jon Hiseman's Colosseum II before earning proper money as everybody's favorite heavy rock keyboard sideman) coming through, he's unleashed with DP and Steve Morse (himself no stranger to prog) is gracious enough to give him all that room. These days, DP is an organ-driven band (more so than they were in Deep Purple line ups of yore with the possible exception of Mk I - Hush era) with a very good guitarist playing contently second fiddle. Deep Purple's sound was always shaped by a Hammond loud in the mix, but Don Airey has upped the ante.
And Gillan's vocal lines which have always avoided the obvious and ear-friendly (to the chagrin of Blackmore) only add to the prog flavor because he only writes them after the band has finished recording its instrumental work completely. They don't "make room" for him. He only recently repeated that DP is essentially an instrumental band and that he "gets to sing a little over their music". He drove Sabbath nuts during the recording of Born Again as they were unused to his process. They would play parts to him and ask him whether he regarded it as a verse or a chorus and he'd say: "I dunno, finish the song, and then I'll decide what to sing."
This song here owes more to ELP once it starts (around 1:40) than traditional DP:
Or this here: