The context makes it evident that «любят» means love here, but is that the only clue for that? Couldn't you think of it being just a "like" case?
It could not, unless You is a nation that your parents like. If "you", however, means a single person, there is no other interpretation here.
It can not be literally translated to Russion. Actualy -
to love is любить
to like is нравится.
Your sentancise can be transtated as "Ты нравишься своим родителям" (You are liked by your parents).
(My native language is Russian, so I'm sorry if I make mistakes in English :) )
I’ll try to explain how. Sorry for my English. This word is pronounced like this ['lyu-byat]
We stress the first syllable "лю" and pronounce it clearly [lyu]. It sounds like the first syllable in "Luminary".
The second syllable "бят" is unstressed and we pronounce it faster. It sounds like [byat]
But If you pronounce "любят" very quickly like here it will be difficult to understand if it's "любят" or "любит". But you can always understand it by the sentence. In this sentence "любит" doesn't work.
Oh, I see. So it actually is "lyo-byat" but with barely audible "y" consonants. Thank! And nice website.