Tic Tac Toe (2 players)
Disclaimer: I only have a TI-85, whose commands are slightly different from the TI-83 and TI-84.

User Experience


At first, I was puzzled by the numbering of the squares.  Then I realized that squares 1 to 9 corresponded nicely to the way the calculator number pad is laid out.  Nice!
You could probably do without the lines at ±9, as a tic-tac-toe board is conventionally drawn as #, with no borders.
There's not much point in asking who goes first, in my opinion.
As you noted, you fail to check whether a square is already occupied.  A nine-element list could easily be used to perform that check.


Code


Variables X and O are defined but never used.
I don't know why you chose to name your variables F and M.  I would have picked P for "player" and S for "square".
The two-argument form of the Input command can also display the prompt.
fPart(M/3)3-2→H didn't work for me.  Due to the way precedence of operations works on the TI-85, it is evaluated at fPart((M/3)3)-2→H.  Rewriting it as 3fPart(M/3)-2→H fixes it.
The code to map M to H and V is excessively complicated.  Each assignment should be done in one line:

6(mod(M-1,3)-1)→H
6 int((M-4)/3)→V


The TI-84 has remainder() instead of mod().
The TI-83 has neither remainder() nor mod(), and must use 6(3fPart((M-1)/3)-1)→H.
I believe the latter is works for all three models.
Your use of Goto is unjustified.  I should be initialized, tested, and incremented using a For( loop.
To toggle F between 0 and 1, just do 1-F→F.  You don't need an abs function.
I'm not sure that ClrDraw adequately resets the drawing context.  On the TI-85, I need ClDrw, ZStd (to set the bounds to the standard zoom), and AxesOff (to hide the axes).


Rewrite for the TI-85 dialect

I've noted what I believe the equivalent TI-83 / TI-84 commands are, based on reading the Guidebooks.

:ClLCD                       Equivalent to ClrHome?
:ClDrw                       Equivalent to ClrDraw?
:ZStd                        Equivalent to ZStandard?
:AxesOff
:DrawF -3                    Equivalent to Horizontal?
:DrawF 3
:Vert -3                     Equivalent to Vertical?
:Vert 3
:1→P
:For(I,1,9)
:Input "Square (1-9)? ",S
:6(mod(S-1,3)-1)→H           See portability note above.
:6 int((S-4)/3)→V
:If P
:Then
:Line(H-2,V-2,H+2,V+2)
:Line(H-2,V+2,H+2,V-2)
:Else
:Circl(H,V,2)                Equivalent to Circle?
:End
:Pause
:1-P→P
:End