Yes, SPLINTERY is a Scrabble word!

Letter values in Scrabble US: S 1, P 3, L 1, I 1, N 1, T 1, E 1, R 1, Y 4.

Is it a valid word?

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

subject to breaking into sharp slender pieces
resembling or consisting of or embedded with long slender fragments of (especially) wood having sharp points

Not playable in Scrabble US: SLIVERY.