Name of this interesting variant of Tic-tac-toe?
BGG doesn't have any game with "Spillage" in the title. Looking at the Tic-Tac-Toe entry there is also no game that reimplements Tic-Tac-Toe which is the same as Spillage. There are a number of games which play some sort of meta-game of Tic-Tac-Toe in which there are nine 3x3 games being played and the object is to get 3 in a row on the meta-board. So all in all "Spillage" would seem to be as good a name as any.

I'd guess that the game is a first player win like the game Hex since having an extra position can't hurt.

Since it is a "new" game it won't have been solved. But writing a program to play would need a dept first approach with symmetry. The look ahead would seem to be fairly uncomplicated so I'd guess that a computer could either win or tie with a decent program. 

Given that the human moves first I'm not sure that a human could out-play a computer on this. If such a winning strategy could be found for the first player then the game would just be a gigantic meta-Tic-Tac-Toe game of course.