Right at the entrance a while interesting, but (I believe) unanswerable question.
Because “Vectrex” is an artificial name for a particular thing. Depending on, to what we expect in the thing, one has a male, female or neutral Vectrex: The game computer, game console, the device.
Even the omniscient Internet is no clear picture, as a search on Google shows:
“die Vectrex”: 979 hit
“the Vectrex”: 839 hit
“the Vectrex”: 806 hit
The former manufacturer MB (Milton Bradley) drops the item off completely and writes only “VECTREX”. So it is, for example, on page 11 German manual “Important notes for the case, that Vectrex is not functioning properly.“. In the use of “Vectrex” as a name that's right, because you write, too “Peter goes home.” and rarely “The Peter goes home.”.
Personally, I only know “die Vectrex” and can not even tell, Though I initially was thinking of the game console. Who's is different usual, just always “the” or “of the” read. 😉