eing one of the most pupular tourist sites in Italy 是v-ing 做状语
而as 是连词,用来联接两句句子,两者只取其一
因此 as one of the most popular torist sites in Italy或being one of the most pupular tourist sites in Italy
前面说到as是连词,完整的表达应该是
As (pompeii is) one of the most popular tourist sites in Italy,Pompeii was viewed by nearly two million visitors last year.
当从句主语与主句主语一致（都是Pompeii)并且出现be动词时,从句主语与be动词可以省略.