Yes, GOVERNMENT is a Scrabble word!

Letter values in Scrabble US: G 2, O 1, V 4, E 1, R 1, N 1, M 3, E 1, N 1, T 1.

Is it a valid word?

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

the organization that is the governing authority of a political unit
the act of governing; exercising authority
(government) the system or form by which a community or other political unit is governed
the study of government of states and other political units

Also: government activity, political science.