The actual pistol in question is not a Stoeger Luger but an Erma. IMHO, the Stoeger is better than the Erma, but it resembles the "real" Luger even less.
The use of the Luger name by Stoeger and not by Erma came about in an interesting way. First, the pistol was never called the "Luger" in Europe; it was always called the Parabellum pistol. "Parabellum" was used by Deutsche Waffen-und Munitions Fabriken (DWM) as a tradename, based on the Latin phrase "si vis pacis para bellum" (if you want peace, be prepared for war). It was also their telegraph address, "Parabellum, Berlin."
Stoeger was the U.S. importer for the commercial pistol in the 1920's and, to keep a distinction between their new pistol sales and the imports of various surplus and reworked WWI pistols, trademarked the name "Luger". So legally, Stoeger and only Stoeger could use that name on or in advertising for a pistol in the U.S. So when they decided to have a pistol made to compete in the .22 caliber market, they had a "sort of" copy of the Luger made, and used that name on it.