Is belief in one who was a prophet but not a messenger obligatory, based on the Hadith of Gabriel which mentioned belief in the messengers among the pillars of faith?

The obligatory faith includes belief in all prophets and messengers, not just messengers. This is a pillar of creed. Allah Almighty says: (Say, "We believe in Allah and what was revealed to us and what was revealed to Abraham and Ishmael and Isaac and Jacob and the Descendants, and what was given to Moses and Jesus and what was given to the prophets from their Lord. We make no distinction between any of them, and we are Muslims [in submission] to Him.") Al-Baqarah/136. Therefore, disbelief in one messenger or prophet is disbelief in all messengers. Belief in all prophets is an obligatory duty, and whoever disbelieves in one of them has disbelieved in all of them. The Hadith of Gabriel, which mentions belief in messengers, also includes prophets. The word "messengers" here encompasses prophets and is used by way of غالب (preponderance), meaning both prophets and messengers.