Calculation of the salience function (Klapuri 2006)
You are correct that STFT is a function of 2 variables (usually x-axis is time and y-axis is frequency). The author is a bit careless in calling $Y(k)$ the STFT. What he really means is that $Y(k)$ is a fixed column (i.e. fixed time slice) of the STFT. The salience function is more carefully defined by the same author in this paper titled Multipitch analysis of polyphonic music and speech
signals using an auditory mode Eq. 13, where he uses a subscript $t$ to denote a fixed time slice of the STFT.