In this paper, the $η$-Nash equilibrium ($η$-NE) region of the two-user linear deterministic interference channel (IC) with noisy channel-output feedback is characterized for all $η> 0$. The $η$-NE region, a subset of the capacity region, contains the set of all achievable information rate pairs that are stable in the sense of an $η$-NE. More specifically, given an $η$-NE coding scheme, there does not exist an alternative coding scheme for either transmitter-receiver pair that increases the individual rate by more than $η$ bits per channel use. Existing results such as the $η$-NE region of the linear deterministic IC without feedback and with perfect output feedback are obtained as particular cases of the result presented in this paper.