I did not know that, thanks! Looking into it, according to Wikipedia it's "operated by a private organization, the Free File Alliance" [1], which is a "public-private partnership with the Internal Revenue Service (IRS) to provide free electronic tax filing services" [2]. The Missouri company you list is one of the "7 participating Alliance members" [2].
I honestly don't know what a "public-private partnership" means, or how that's different from the IRS just contracting a company to build a product. But it seems awfully integrated into the IRS's website, so there's clearly a "partnership" -- it can't be total randos (hopefully??).
I don't see any obvious red flags in the privacy policy, is there something to be worried about?
[1] https://en.wikipedia.org/wiki/Free_File#Free_File_Fillable_F...