As long as it doesn't take the wing most aircraft are pretty safe on reduced power. At least, they used to be. Wouldn't trust one of the pajeet-designed ones today.
This 777 was the fifth (IIRC) one off the line in 1994, and the third oldest still in service. Well before pajeets came into the picture.
And yes, modern twinjets can fly and even climb on a single engine. The 777 in particular was one of the first aircraft with ETOPS 180 certification, meaning it's allowed to fly over-water routes where they could be up to three hours away from a suitable airport on a single engine. The plane in question was on the way to Hawaii.
So no, this wasn't a design issue. This was most likely a maintenance fuck-up on United's part, or on Pratt & Whitney if the engine is fairly new (i.e. not original to the aircraft).
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