Does "not so fast" spell can block the play effect of Thousand-tail Watcher?

No, you cannot use Not So Fast to counter the "When you play me" ability of Thousand-Tailed Watcher.

According to the official ruling:

• Not So Fast requires the enemy spell or ability to "choose" (target) a friendly unit or gear.
• Thousand-Tailed Watcher's ability applies a blanket effect to all enemy units simultaneously. Because it does not target or choose specific units, it does not meet the requirements for Not So Fast to be played against it.