Tic-Tac-Toe redux

In December 1985, the french magazine Science & Vie #819 listed several variants to be played on the standard 3x3 board of Tic-Tac-Toe. 

Here are some:

• Decentra: the first player cannot play at the central square. Does the second player wins by playing himself there?
• Misera or Toe-Tac-Tic: this is the misère variant, the one that makes a 3 in-a-row loses
• Doulima: each player must place one, two or three pieces or either color on a given row or column; the last player to move wins
• Nullita: game is played normally, but one player wins if any 3 in-a-row is made (of either color), while the other player wins otherwise
• Toucha: the first player forced to place a piece touching one of their own on a horizontal or vertical side loses the game.
• Connecta: this is the opposite of Toucha, the first player placing an isolated piece (ie, not connected to any friendly pieces) loses (except for the first turn).

The article has even more variants:

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Another, older, variant of Tic-Tac-Toe is 1943's Tic-Tac-Tics by Henry Lewis which uses a score approach. The game is played on a 5x5 board, where each 3, 4 and 5 in-a-row scores an increasing amount of points:

  

Even with the central placement restriction for the first player, there still might be an advantage to start. One possible approach, simpler than the 'inning' system the rules propose, is to play just two games, where each player starts in one, and sum the two scores to decide the winner.