Yes, WATCHING is a Scrabble word!

Letter values in Scrabble US: W 4, A 1, T 1, C 3, H 4, I 1, N 1, G 2.

Is it a valid word?

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

look attentively
follow with the eyes or the mind
see or watch
observe with attention
be vigilant, be on the lookout or be careful
observe or determine by looking
find out, learn, or determine with certainty, usually by making an inquiry or other effort

Also: watch over, keep an eye on, take in, look on, look out, watch out, find out.