The window opened very easily. Clay needed barely to touch it, and it opened.
The meaning is most likely not literal. Clay might've made a more comprehensive movement than just a single touch to open the window; but that is irrelevant for this narrative; the author needed to stress the fact that it opened easily.
From the grammar standpoint, touch is a noun, a singular countable noun, as evidenced by the use of the indefinite article a. "The window opened at one touch", or "at a single touch".
Compare with the expression at a glance:
At a glance: (idiomatic) Upon cursory examination; an abbreviated review. "At a glance it seems that he is a nice guy, but upon digging deeper the truth emerges."