My PhD thesis does not include a Literature Review chapter
This is a question for your advisor. What will s/he accept in your dissertation? If it is a acceptable to the advisor (and any committee) then there is no issue at all. 

It seems pretty clear from what you write that you have, in fact, reviewed the literature, rather than just ignoring it. How you present your findings is, in a sense, just a matter of writing style. If it works, it works. 

But your advisor may have veto power here, so make sure they are happy.