如果riding是動名詞
I don't like the boy riding my bicycle.
boy名詞,又接riding動名詞
整句沒有連接詞,很明顯是錯的

應該解釋成
關係代名詞who引導的形容詞子句who is riding my bicycle
who省略,is省略
只留下riding my bicycle
來形容the boy
所以2.才是正確的

現在分詞&動名詞兩者的差異?
現在分詞=動詞的現在式 -> He is "riding" my bicycle.
動名詞=名詞(通常指一件事or物) -> Riding bicycle is interesting. = To ride bicycle is interesting.