The Gay Nineties are the 1890s, or more specifically, the genre of fiction from the 1930s and '40s set during the 1890s. Both the real King In Yellow and the fictional King In Yellow were written in 1895, intimately tying them to this decade. Interestingly, some of Robert W. Chambers' stories in the collection look towards the period in which nostalgia for the era in which he was writing began to grow.
The genre is something of a precursor to that of steampunk.
See also Roaring Twenties