Yes, ESTABLISHMENTS is a Scrabble word!

Letter values in Scrabble US: E 1, S 1, T 1, A 1, B 3, L 1, I 1, S 1, H 4, M 3, E 1, N 1, T 1, S 1.

Is it a valid word?

ESTABLISHMENTS is a valid word in the official Scrabble dictionary (US), the UK Scrabble Dictionary and Words with Friends (ENABLE).

the act of forming or establishing something
an organization founded and united for a specific purpose
the persons (or committees or departments etc.) who make up a body for the purpose of administering something
a public or private structure (business or governmental or educational) including buildings and equipment for business or residence
any large organization
(ecology) the process by which a plant or animal becomes established in a new habitat
the cognitive process of establishing a valid proof

Also: governing body.