Who coined the term "empirical entropy"?
I am interested in "empirical entropy" like you and the earliest paper I find was that from Kosaraju like the user "Marzio De Biasi" told in his comment.

But in my opinion the real definitions of "empirical entropy" are made later by generalizing the former concepts: 


"Large Alphabets and Incompressibility" by Travis Gagie (2008)  
"Emprical entropy" by Paul M. B. Vitányi (2011)


Gagie rephrase the definition of $k$th order empirical entropy to:  


$H_{k}(w)=\frac{1}{|w|}\min\limits_{Q}\left\{\log\large\frac{1}{P(Q=w)}\right\}$


where $Q$ is a $k$th order Markov process. He also showed that this definition is equivalent to the previous one.
The next step from Vitányi was a generalization to arbitrary classes of processes (not only Markov-processes):


$H(w|\mathcal{X})=\min\limits_{X}\left\{K(X)+H(X):\;\left|H(X)-\log\large\frac{1}{P(X=w)}\right|\normalsize\;is\;minimal!\right\}$


where $\mathcal{X}$ is the class of allowed processes and $K(X)$ is the Kolmogorov complexity.
If we choose $\mathcal{X}$ to be the class of $k$th order Markov processes producing  a sequence of $|w|$ random variables and ignoring the Kolmogorov complexity, than this also leads to the definition of Gagie (multiplied with $|w|$).