Do ALL living organisms have intestines?

No, but some don't have the guts to admit it.

A through gut is only found in animals as highly evolved as the earthworm - so jellyfish, corals, sponges, tapeworms etc only have a sac-like gut. No intestines and no anus.
https://www.bbc.com/earth/story/20150313-the-origin-of-the-anus

There is one relatively highjly-evolved animal that has such an efficient metabolism and limited diet it needs no excretory organs at all. I assume it transpires its waste - (just water and carbon-dioxide?) - through its skin.

That animal is the "Eyelash Mite", a microscopic inhabitant of the gap between hair and follicle wall, where it dines royally on sebaceous oil.