I wd keep the article... Me gusta el ciclismo de pista. It's just un-grammatical otherwise. But as LBTrek says that's exactly the same as "I like track cycling"; you cd be a rider or a fan.
I like to race track wd be "Me gusta competir en (carreras de) ciclismo de pista"
I like to ride track... I'm not sure. "Me gusta montar en bicicleta en la pista/en el velódromo" sorta means that but it sounds clumsy to me.

(Stragely, they often use ciclismo en pista, too.)

BTW, machine translators are so funny... Quiero means to be in love with, and then I have no idea how vestigio came in... that means "trace" (vestige). Perhaps you made a typo.