The 29-year-old world number 21 took the first game 12-10 after an impressive trick-shot between his legs with the scores tied at 10-10.
But Egypt's 2014 US Open winner edged the second and third games 11-9 and 12-10 before winning the fourth 11-5.
Simpson had beaten Egypt's Karim Ali Fathi in the opening round.
"Played my first trick shot today. Wanna know how I did it? Me too....," Simpson wrote on Twitter after the match.

Frank MacDonald, 44, from the Brechin area, was between the B976 South Deeside Road at Strachan and the B974 Cairn o'Mount road at about 14:00 on Saturday when the crash happened.
The vehicles involved were a blue Suzuki GSXR motorcycle and a grey Toyota Hilux.
Relatives said the "much loved" father-of-three would be greatly missed.
The unclassified road was closed for more than eight hours following the crash. Police have appealed for witnesses to come forward.
Guernsey's Chris Simpson has been knocked out of the US Open, despite pushing world number one Mohamed El Shorbagy in their second-round tie.
[NEXT_CONCEPT]
A man who died after his motorbike collided with a car in Aberdeenshire has been named.