How do we get to Mongkok Station from airport express if we choose to ride the train all throughout?

If want to take Airport Express, you can take it to raech Tsing Yi and then change to Tung Chung Line to reach Lai King where you can change to Tsuen Wan line to reach Mong Kok directly.
In my opinion, it is not necessary to take the Express. You can take airport shuttle bus S1 to reach Tung Chung where you can take Tung Chung Line to reach Lai King and then change to Tsuen Wan Line to reach Mongkok which is much cheaper than taking airport express.