This is based on an idiom which came from a quote, modified from another quote… [bear with me].
There's a saying,
One swallow does not a summer make
which is the direct usage your example is drawn from. The connotation of the original is that just because one good thing has happened, does not necessarily mean others will follow as a natural progression. This usage is thought to have originated around 1920
It's thought the odd word order of "one x does not a y make" is itself drawn from a 17th century poem - To Althea, from Prison by Richard Lovelace
Stone walls do not a prison make,
Nor iron bars a cage;
One could say the structure is antiquated, archaic. It seems to survive only in that form, ending in 'does not a y make'. Once something becomes idiomatic in that way, whether or not it is strictly grammatical becomes moot.