Question

Is this sentence correct as written?

Answer 1

Yes this is grammatically correct

Answer 2

This sentence is grammatically correct.
 It might sound strange because the subject is not written, however, it is not necessary in Spanish. You can guess the subject by the inflection in the verb. 
The verb "Tienen" reveals that it is a 3rd person/plural subject. So you can also say " ELLOS tienen que cuidar a sus abuelos"