You have a few errors:

The timers do not turn off when the word is said or the stopguess occurs.

If you do not have halfop or op you will receive an error.

I edited your code a bit. I fixed the timers by adding a .timersay off. Try this:

on *:TEXT:*:#:{ 
  if ($1 = !guessword) && ($gettok(%gamestatus,1,32)) { 
    if ($2 = %word) { 
      set %win on 
      msg $chan $nick has won the game!
      if ($nick !isvo $chan) && ($me isop $chan) { mode # +v $nick }
      .timersay off
      halt
    }
  }
  if ($1 = !stopguess) && ($gettok(%gamestatus,1,32) = on) { 
    unset %gamestatus
    msg $chan Guessing game has been stopped.
    .timersay off
  }
  if ($1 = !startgame) && (!$gettok(%gamestatus,1,32)) { 
    unset %hintstatus
    unset %win
    set %gamestatus on
    msg $chan Guessing game has started.
    .timersay 1 5 msg $chan Hint: %hint1 
    if (%win != on) { 
      .timersay 1 30 msg $chan Hint: %hint2
      .timersay 1 50 msg $chan Sorry, your time is up! The word was %word $+ .
    }
  }
  if ($1 = !neword) && ($nick iswm %owner) { 
    msg $nick Please enter your word and hints.
  }
}

on *:TEXT:*:?:{ 
  if ($1 = new) { 
    if ($2 = word) set %word $3
    if ($2 = hint1) set %hint1 $3
    if ($2 = hint2) set %hint2 $3
  }
}

Otherwise, not bad. I recommend a little more work put into this. Maybe use a text file to read different words or make it into something bigger such as a scramble game.