Once you authenticate yourself to the store (i.e. sudo snap login) you can then install snaps on your system without needing root privileges.
You can check your current authenticated user with snap whoami and it will show the email address associated with your device. An unauthenticated user would see an empty email, like:
email: -
and will then need root privileges to install a snap.
All of this is true if you’re installing snaps on bare metal, KVM or a LXD container.