different than an ARC?  It doesn't say anywhere on the cover that it's an ARC, just that it's a "free" copy.

I'd post it.  A free or complimentary copy is not the same as an ARC.

Unless it says it's an Advance Reader Copy or Uncorrected Proof, it's probably fine to post.  Lots of books are issued as free copies for one reason or another, but as long as it's a "final" version, it's ok to post.

I would check the copyright page for a notice saying the book differs from the original. (Very common in Harlequin freebies, which are often edited.) If it has one, I personally would not in good conscience post it.

I'd assume a "free" book is like ones that sometimes come in kids' meals at fast food restaurants or sent as a "premium" for buying diapers or cereal--- or given as a promotional item at a community event (like literacy projects often do). I would expect an imprint on the book, possibly the cover, stating the name of a product vendor who paid for the printing of the book (such as Huggies or Pampers for a potty training book).