With the HTC wall charger your phone (without using) should fully charge in 2.5 hours.
So maybe the wall charger is faulty.
The 'Battery Monitor Widget' on my Sensation shows my the charging and discharging current of the phone in a graph.
An almost empty battery in stand by, the wall charger should charge with up to 800mA - 900mA.
Worth a look could be the discharging current of your game.
So play for a while without charging the phone and look afterward at the current graph.
So you can compare charging and discharging current of the battery.
It's an easy calculation:
If you want to play while charging the charging current have to be bigger than the discharging current.
But playing while charging shouldn't be a problem.
I charge my Sensation successfully in the car while running a very power consuming navigation app
EDIT: Maybe the first step to check the wall charger: The phone should "Charging (AC)", not "Charging (USB)".
To look at > Settings > About phone > Battery > Battery status ...
"AC" means up to 1000mA
"USB" means up to 500mA