Simple mov·i is a transitive verb meaning “to move an object to another place, to change a position of something”. And therefore you have to say mov·iĝ·i, which means “to be moving, not to rest in one's previous place or position”. So bovinoj moviĝas exactly means, that these cows are moving by themselves, without anyone's help. :)
Because that is not a correct translation. ;)
The English noun “bovine” is “an animal of the biological subfamily including cattle, buffaloes and bison” and there’s much difference between a member of the subfamily Bovinæ and the meaning of the Esperanto word bovino, which not only is restricted to the species Bos taurus (cattle) but, more importantly, refers only to female members of this species (so cows).
While learning the word bovino, keep in mind both the word “bovine” and “beef” as a good memorisation help, but don’t trust those associations too literally. :D