I don't believe it is a sequel, rather, the "death game" (SAO style) Shin was trapped in before the main plot of TNG opens is just background. "The New Gate" itself may refer to either the gate that opens when he defeats the "boss," or perhaps another gate that might be in the world that may take him home.
You can read the LN here: https://shintranslations.com/the-new-gate-toc/. I've read the first three volumes, and there is no indication that TNG has another story (of the death game) before it. That doesn't in any way rule out the author writing a prequel, but I believe it's currently the end-all and be-all of it's story arc.