Simply defined, it was a system for structuring society around relationships derived from the holding of land in exchange for service or labour.
This certainly doesn't seem to apply. While the Maiar did give service to (or were in the service of) certain Valar, there's no evidence that they held land in exchange for it. In fact the service they gave seems to have been more a form of assistance, based on a less complete but more focussed understanding of the nature of creation.
A closer analogue (I don't pretend it's perfect) might be an assistant to a master craftsman: the assistant might know how to do one part of the job really well, better than the craftsman even, but only the craftsman knows the whole.
Now looking at the spiritual, rather than the functional, side of this relationship, in his Letters Tolkien describes Gandalf in particular in the following terms (Letter 181):
His function as a 'wizard' is an angelos or messenger from the Valar or Rulers...
I've emphasised "angelos" here because it's almost certainly not a casual use of the word, and may be said to definitely suggest "angel", as viewed and interpreted by a Catholic writer. Letter 131 goes on to confirm this:
The cycles begin with a cosmogonical myth: the Music of the Ainur. God and the Valar (or powers: Englished as gods) are revealed. These latter are as we should say angelic powers, whose function is to exercise delegated authority in their spheres...
The relationship of the Valar and Maiar is therefore clearly an analogue of angels and archangels in Catholic theology, rather than anything else.
This passage is also important because it mentions the function of delegated authority, but that would require further discussion beyond the scope of this question.
Gandalf is also an interesting case, because he shows that individual Maiar were not "bound" to individual Valar. Gandalf was in the service of Manwe, but also spent a lot of time in the gardens of Lórien (his name contains the same linguistic elements: Olórin/Lórien) and learned a lot of pity from Nienna.
So no, there was no feudalism (or even pseudo-feudalism) here.