No, you don't "have" to do that. Will SOME games perform better with 16GB? Absolutely.
Is it "mandatory"? Not really. There are always ways to get by with what you have, even if it means moving some sliders or choosing presets that are not overly taxing for the configuration that you have. Not every person needs to play every game at max settings in order to have a good gaming experience.
There are also many other factors involved such as the number of background programs you typically have running, how clean the OS installation is and whether you have fast storage or old slow mechanic spinning drives. These things can all play a role, but any configuration can be tailored to work. Some will clearly be better than others, and there...