According to default sources, Gen Fu fought in the DOA Tournament to obtain the cure needed to heal his sick granddaughter Mei Lin, who was suffering the ravages of a rare disease. In DOA2, he wanted to fight Bankotsubo for his nose of legend that says it can cure any disease.
However, that didn't happen due to Hayabusa defeating Bankotsubo. But in the 4th tournament, Gen Fu obtained the money for Mei Lin and currently she is making a steady recovery, so he had no interest in participating for the 5th tournament other than training Eliot as his apprentice.
Given how video game companies like to create characters then forget them (resulting in the issues with Sonic the Hedgehog) i'm gonna say they totally forgot her.
Actually, it would be no surprise if they did include to make the character early. Given to how TN usually takes a ton of time to create new characters.
It's the moment of - Head: "Alright, we can't think of any new characters, what do we have so far? - Staff: Miyako, Mei Lin, Muramasa, Genra, Shiden. Head: "Who's the least talked about?" Staff: Shiden and Mei Lin. - Head: "Who's important? Staff: Uh.... - Head: Wait, is Shiden the one who has an unimportant son? Staff: Yes.