This has nothing to do with singular/plural and everything to do with verb conjugation, mostly because like, as it's used here is a verb, not a noun.
- "He likes to watch movies"
- Third person singular present tense.
- "They like to watch movies"
- Third person plural present tense.
- You like
- Second person present tense
- "He doesn't like to watch movies"
- "He does like to watch movies"
- "Does he like to watch movies?"
- All three of the above are infinitive.