Yes, TIGHTER is a Scrabble word!

Letter values in Scrabble US: T 1, I 1, G 2, H 4, T 1, E 1, R 1.

Is it a valid word?

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

closely constrained or constricted or constricting
pulled or drawn tight
set so close together as to be invulnerable to penetration
pressed tightly together
(used of persons or behavior) characterized by or indicative of lack of generosity
affected by scarcity and expensive to borrow
of such close construction as to be impermeable
of textiles
securely or solidly fixed in place; rigid
(of a contest or contestants) evenly matched
very drunk
exasperatingly difficult to handle or circumvent
demanding strict attention to rules and procedures
packed closely together

Also: blind drunk, pie-eyed.