A spectator is living.
The creature feature that allows a monster to function without food or drink is generally reserved for Undead, Constructs or Elemental creature types.
Undead Creature Types
Crawling Claw, Mummy, Skeleton and Bone Naga are some examples of undead creature types from the MM that require no food or drink (or air or sleep). Even Zombies in D&D 5e require no food or drink - no brains for D&D zombies.
Death Knights are the only undead in the Monster Manual that do not have this feature. They apparently require food and water. Will-O'-Wisps do not need drink, sleep or air, but they do feed on fear.
Construct Creature Types
Constructs are made, not born (MM 6) and often do not require food or drink (or air or sleep). Golems, Animated Objects, Scarecrow and Shield Guardians are some creatures of the Construct creature type from the MM that do not require food or drink.
Homunculus and Modrons are the only two constructs in the MM that do not have this feature. They do require food and drink.
Elemental Creature Types
Elemental creature types also generally do not need food or drink. This includes Elementals, Water Weird, Mephits and Azers and others in the MM.
Genies, Salamanders and Xorn are the only Elemental creature type that do not have this feature.
Other than powerful immortal beings, like Angels there are no other creatures that can survive without food and drink.
What about the Spectator?
A Spectator probably doesn't have this creature feature because it doesn't fit in with the general standards established in the MM for creatures with this feature. It's partially an issue of narrative, and partially an issue of consistency.
A Spectator is not of the Undead, Elemental, or Construct type. They are just badass and can conjure themselves all the food they need. This is probably necessary because they have to hang around one spot for 101 years guarding some treasure they've been summoned to protect.