SQL - Update table for a unique ID with multiple entries if one entry has variable in question
There multiple entry in table patient_encounter for a person_id, so you need to get the person_id with top 1

Try this

update patient_encounter 
Set user_defined4 = 'DTC'
where person_id = (SELECT top 1 person_id from patient_encounter 
                     where  mrkt_plan_id = '489681B4-9D94-413B-95A0-C50D5964F340')


EDIT as per comment, if you are looking to update all the record, use IN as below

update patient_encounter 
    Set user_defined4 = 'DTC'
    where person_id IN (SELECT person_id from patient_encounter 
                         where  mrkt_plan_id = '489681B4-9D94-413B-95A0-C50D5964F340')