You have 3 slots plugged in the principled BSDF, this means you will need to bake each of the 3 to a texture.
The easiest way to bake any part of a material:
1- Set the bake type to emit.
2- Take the wire that goes into the base color slot and plug it directly into the material output node, where the principled shader is going right now. That’s going to display whatever you have for the color slot as a flat emissive material (colors without lighting).
3- Bake the result. You can reduce the render samples greatly for baking. If you aren’t using any AO, Bevel nodes or lighting as part of your material, you can even set the samples to 1, as it makes no difference for the quality.
4- Repeat the same steps, but plugging the metallic, then roughness wires into the material output.
5- Now, you could remove the entire material setup and replace the color, metallic and roughness node structures with the 3 textures you baked and you should get the same result from those new textures. You can also bring those textures in a game engine and plug them in the material there in the same way. Materials don’t transfer between softwares as there is no full standardization, but you will be able to easily re-create the same material, as everything has been turned into 3 textures you can just plug.
You didn’t specify, " What Game Engine?" that can make a big difference to your workflow, and requirements.