After you shoot those bullets and need to reload, what happens to the old clip? Does it pop out the bottom of the magazine part when you put in the new clip?
Its a stripper clip. Starting from the position in the picture, you would push down on the bullets and they "strip" (or slide) off the clip into the magazine. You're left with an empty clip sticking out the top of the gun which you lift away and throw at the enemy or your buddy or whatever. If you want to look up a video, they're commonly used on the SKS.
En-bloc clips also exist. Those do go into the gun like you're thinking, but they actually eject out the top when you fire the last round. Like the M1 Garand from any WWII game.