Boy this must have been good stuff!!
The J. Stevens Arms & Tool Co. No. 105, 107 & 115 singles were listed with Electro Steel in 1901. In 1902 the No. 180 hammerless single had
Special Pyro-Electro Steel.The Iron Age, April 1902
https://books.google.com/books?id=xqM-AQAAMAAJ&pg=RA9-PA65&lpg The first electric arc furnace was developed by Paul Hroult, of France, in 1900. Hroult came to the U.S. in 1905 and Halcomb Steel Co. installed the first electric arc furnace in the U.S. in
1906 (4 years after the Stevens ad
)
Blast Furnace and Steel Plant, November 1922
https://books.google.com/books?id=ad0fAQAAMAAJ&pg=PA542&lpg Electrically refined steel, or electric steel, or electro steel was reported to allow a higher carbon content with less sulfur and phosphorus compared to Crucible or Open Hearth process steel.
The Horseless Age, Dec. 14 1910
https://books.google.com/books?id=DKONYWNYDqIC&pg=PA813&lpg Chiltons Automotive Industries, January 12 1911
https://books.google.com/books?id=sB1HAQAAMAAJ&pg=PA137&dq Sanderson Brothers Steel Co. installed an arc furnace in 1907. This furnace is now on display at Station Square, Pittsburgh, Pennsylvania.
I'm thinking the "pyro" & "electro" part came from Stevens' marketing dept.