All airliners must be able to take off at MTOW, cruise and land with one engine inop.
Normally the runway won't be long enough for the take off. But when one engine quits after V1 speed it must be able to accelerate to VR
speed and climb out.
Of course it will climb much less steeply. And it will not cruise at high altitudes.
The latter is also because with only one engine running you will lack redundancy on air conditioning and cabin pressurization. A twin on one engine will normally cruise at around 10,000 feet for safety reason - should the aircon fail on the lone remaining engine.
At 10,000 feet any twin including the 777 will cruise brilliantly on one engine at nowhere near max power. But it will cruise somewhat slower due to the thick air, and that's the main reason why it will have considerably reduced range on one engine.
A nice and clean airliner as the 777 will with one engine windmilling have a lift to drag ratio around 16 - 18. That means for instance that if we assume an actual weight of 500,000 lbs it will need 30,000 lbs thrust for level cruise. At low altitude that is roughly half power from one engine only.
In fact it will need at much higher power setting for cruising on two engines at 40,000 feet. But that's because at such high altitude, and consequently the thin air, the available power is reduced by some 70 - 80 percent.
The 6 hours "test" on one engine tells nothing. Any 777 out there is able to cruise for 15 hours on one engine. And if it isn't, then something is seriously wrong and that particular plane should never be allowed to be moved anywhere near a runway with the intention to take off on its two engines.