You need to be a member. That provides member ID.
I am also not sure if they can provide the service FROM the airport, as any taxi except the Airport taxis is not supposed to be allowed to wait in the area.
If you live in Taiwan, and leave FROM Taiwan, then when you go to the airport they book it, as then they get your flight number and can arrive just in the nick of time, without waiting.
Options? Uber or Airport taxi. The second one is more expensive.
BTW, that page is from my favorite taxi service, Taiwan Taxi.