I don’t know any plugin that allows that. Anyway, there are other options to let users upload videos to your webpage.
I would make a new user Role. You can install User Role Editor plugin to do that. After creating a new Role, you can give the permissions you want. You can allow them to use some resources of the backend, while you keep the rest out of their reach. If you are using a plugin to manage your multimedia section, you should give the permissions to use it.