Is this Monogatari opening a take on another artists' style?
The OP is not a parody of one series per say, but reminiscent the stereotypes of 80s/90s anime themes in general.

Kindaichi Case Files

https://www.youtube.com/watch?v=SjIXE-YWMHM

Cardcaptor Sakura

https://www.youtube.com/watch?v=UQjCFvaNwJQ

Escaflowne

https://www.youtube.com/watch?v=jbhcChdCAUk

One of the most notable parts (with the hat flying off) somewhat resembles Kimagure Orange Road and/or the Ranma 1/2 OAV OP "Love Panic" (Koi da! Panikku):

https://www.youtube.com/watch?v=777YtDfbnYI

Some sequences are a bit reminiscent of the Golden Boy OP:

https://www.youtube.com/watch?v=47Hg0QIo1x8