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For example, the ibmqx2 computer has the most recent readout error of $4.40 \cdot 10^{-2}$. Does this mean per 1000 measurements, 44 faulty results exist?

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According to [1]:

Readout error is the error in measuring qubits.

You read the figure correctly (44 out of 1000 measurements fail on reading). Note there is yet another, though minor, error there: gate error. It is about errors in quantum gate operation, and is one 10th less than the error of measurement. So, actually there may occur more erroreus results than 44 in total due to the other type of error(s).

[1] https://medium.com/@jonathan_hui/qc-quantum-programming-implementation-issues-51e3a146645e

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