What does "except East Rail Line First Class" mean for Hong Kong Airport Express Travel Pass?

Yes, you are right. The east rail line offers two classes of seats, the first class and the second class seats. If you take it with tourist day pass or other travel pass, you can only use the second class seat. With such a card, you can surely take the MTR from Hung Hom to Mong Kok or Kowloon Tong and vice versa.