At the start of WWII, only two major nations issued a semi-auto rifle, the U.S. and the U.S.S.R. The U.S. rifle, the M1 (Garand) was well developed, and mass production was underway, but the Soviet rifles were still not fully developed and the production facilites, interrupted by the 1941 German invasion, never were able to make enough semi-autos to equip the huge Russian armies. That is one reason the Russians turned to the simple and easy to produce submachinegun to arm so many front line troops.
In Germany, Hitler discouraged research and development of semi-auto and selective fire rifles believing, from his WWI experience, that the bolt action "carbine" was perfectly adequate.
Nonetheless, the Germans made and issued three semi-auto rifles. The first two were the G.41M and G.41W, the letters standing for Mauser and Walther respectively. Both rifles were issued for what amounted to extended troop trials, and the simpler Walther offering became the basis for the G.43.
The G. 43 itself was not a fully developed design, being rushed into production, but it had advantages and was issued in large quantities.
Regardless, the outcome of WWII really was not much affected by the small arms used. The Allies did not win because the U.S. had the M1 rifle, or the Russians had the SVT 40. The huge technological advantage the U.S. had in mass production and the advantage the Soviets had in both production and manpower would have made the difference if all the armies had had only bolt action rifles. When a squadron of P.51's descended on a German troop convoy or a supply column with all guns blazing, it didn't matter much whether the Germans had K.98k's or G.43's, they were in deep trouble.