StringCases use of StringPattern can also pull out matches with sub-strings
StringCases[yourlst, "{8" ~~ __]
{{}, {}, {"{80016}"}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}}
StringCases[yourlst, "{" ~~ num : ("8" ~~ __) ~~ "}" :> num]
{{}, {}, {"80016"}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}}
Flatten to get rid of empty sub-string results
Flatten@StringCases[yourlst, "{" ~~ num : ("8" ~~ __) ~~ "}" :> num]
{"80016"}