Step 1: Create an integer array (one slot for each player)
Step 2: Whenever a player issues any type of order, store the time on the global game timer (which DotA has to tell you how long the game has been) into that player's slot on the array.
Step 3: Every <interval>, detect whether the last order issued was more than 10 minutes before the current time listed on the timer. If so, activate the kick trigger for that player.