Yes? That's intended. The launcher closes once the bootstrapper(cmd) pops up. Is there a specific error you're getting or is it just stuck on the cmd window? If its the first, please screenshot your error. If its the latter, do this and make sure there's no other program running in the background which may interfere with pluto such as overlays.
Regarding this
There is no way to install BO2 again
Don't you have the basegame downloaded? Follow this guide: https://forum.plutonium.pw/topic/2819/how-to-install-update-plutonium-t6