Autothrottle wake-up is a customer option. Based on that, it is possible that not all 777's have it.
The only state where the autothrottle wakeup function is potentially active is when there is no mode. There is no mode when the display on the FMA for the autothrottle mode is....blank. But if it is blank and you are also in FLCH or TOGA, A/T wake-up will not activate when the other required activation conditions are met.