Well, the only man-portable anti-tank weapons with a range greater than 10-15m back in the late 1930's and in 1940-42 were anti-tank rifles. AT-rifles were still rather effective in 1939 for instance, with the average armour of a tank being between 15 and 30mm. By 1940 they were already starting to get useless, by 1942 they pretty much were useless against most tanks.
Nations started to develop different AT weapons as soon as it got obvious that armour would soon outclass any AT-rifles, this first manifested in various AT-grenades like the RPG-40 which were based on pure explosive force or later, hollow-charge AT-grenades. But all of these only really gave the infantry desperate self defence capability and the infantry soon was calling for man-portable anti-tank weapons with a sufficient effective range to enable them to be used offensively.
After that, the age of recoilless AT weapons such as the Bazooka or the Panzerfaust dawned. They were more effective against armour, had sufficient accuracy for ranges between 30-100m and were WAY cheaper to produce. The Soviets never developed or produced anything like them though.
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Why you don't see AT-rifles in games:
First of all, most WW2 games take place between 1943 and 1945, completely neglecting the "age of the AT-rifle". By then, most armies completely removed their AT-rifles from frontline service. The Soviets kept on using them since they still served some purpose on the battlefield (like shooting up optics and vision-slit glass) and they were desperately short on weapons until early 1944. The Germans converted their AT-rifles to grenade launchers, although that only was a stop gap measure to increase the AT-capability by using hollow charge rounds with penetration capability of up to ~80mm.
Since most WW2 games don't care about history or anachronism, they'll happily hand out Panzerschrecks to Germans in Stalingrad. Also, "Rocketlaunchers" (not the correct term for the Panzerfaust btw) are simply "cooler".
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PS: This is just a brief post about the history and thoughts at the time, I wrote it quickly from memory and I'm pretty sure I left out a lot of important stuff and it's riddled with errors. So if you find something that's wrong, feel free to correct me.
