It's true that the categorization describes things that are relatively old because one can track the generations backwards fairly easily, but no one was like "oh man, look at those amazing fourth-gen graphics!" when busting out Street Fighter II on the SNES in 1992. Kind of like how we can describe Cleopatra as being born 69 BCE.

If you absolutely need to discuss console generations and you don't like my idea of simply putting the Wii/Wii U/NS each into two generations, and you absolutely need to use numbers in your discussion, you could always just use the year, or a range of years.

Even then it's a highly-contextualized distinction. PS1/N64/Saturn games all kind of had a certain "look" to them, and there wasn't a huge difference between the hardware requirements and visual fidelity of a high-budget vs. a low-budget game in that era. But nowadays you can have God of War: Ragnarok and Skylight Freerange 2: Gachduine on the same machine.