The Smith and Miller patents were issued October 19, 1886. As mentioned earlier these patents were assigned to both Geo. Duncan & Sons and Bryce Bros. Based on the colour your shoe/slipper was likely made by Bryce Bros. prior to 1887 although these little pieces were made for many years after that.
The company history according to Welker's Pressed Glass in America is:
Bryce, McKee & Co. 1850-54
Bryce, Richards & Co. 1854-65
Bryce, Walker & Co. 1865-1882
Bryce Bros. 1882-1891
Joined US Glass 1891 as Factory B
What were these pieces? The catalogs just called them slippers, some of the wholesaler catalogs suggested toothpick or match holders. Some were sold with perfume or other products in them. Some are seen with advertising for shoe companys so they were likely given away as promotional material.
The book "Shoes of Glass 2" is an excellent study of this collecting area with lots of good pictures, writeups describing old and repro and old catalog cuts.