Verified answer

Not with anything approaching currently available technology or understanding of physics. The plasma gun supposedly shoots a ball of plasma that somehow stays coherent until it strikes its target. The closest thing that exists in nature is "ball lightning". However, even "ball lightning" remains unexplained.

The issue is that plasma is just a fancy name for a super-heated ball of gas. I mean totally super-heated as in thousands of degrees of heat. It is certainly possible to create such a plasma, however, we have no way of containing it in a "ball" to "fire" it at a target. As soon as the plasma leaves the heating container, the hot gas will immediately dissipate. Science fictions says that you somehow create a semi-stable magnetic field that encases the plasma long enough to make it hold its shape long enough to fire it. Nobody knows how this would be achieved. Because, again, a magnetic field only persists as long as there are magnets to support it.

Lastly, the other huge problem with any kind of high energy weapon that is "hand-held" is we have no idea how to make that much energy and store it in a small enough package to make it portable. No battery or capacitor can do it. No nuclear energy technology exists that would allow for that much energy to be generated without throwing off enough radiation to kill the person carrying the weapon. Fission nuclear reactions and fusion nuclear reactions both throw off huge numbers of high energy neutrons. Neutrons are incredibly difficult to shield. It usually requires many feet of water or concrete. There is just no way to carry around the necessary shielding.

So, to answer your question, NO there is no possible way to create the plasma gun as seen in the Doom video game given the current level of knowledge available to humans.

Both are likely possible, but likely not practical. Neil