With Rasbian of 2018-11-13, I had the same issue. So I installed only npm,

sudo apt-get install npm
sudo npm install -g npm@latest

Also I used the pre-built node which is 8.x in the latest version of Rasbian.
While I install, I made a video and please check https://youtu.be/UBgH5hejYtM.

Thanks,

Dependency Versions

1. OS : 2018-11-13-raspbian-stretch-full.img
2. MagicMirror2 : 2.5.0
3. MMM-Hotword : 1.1.0
4. MMM-AssistantMk2 : 2.1.2

Although now I am forced to use no Open GL driver for the MM to start up properly…well hopefully electron still doesn’t use massive amounts of CPU power to run without it now.

Instead, remove/purge Node.js and grab latest, as @Mykle1 suggests:

sudo apt-get remove --purge nodejs
sudo apt autoremove
curl -sL https://deb.nodesource.com/setup_8.x | sudo -E bash -
sudo apt-get install -y nodejs

This should install Node.js and npm. Once the installation finishes, sanity check the install with the following commands:

node -v
npm -v

Then, delete the MagicMirror folder from your previous installation attempt:

rm -rf ~/MagicMirror/

And try the MagicMirror installation script again.
It installed successfully for me after this. Raspberry Pi 3 running Raspbian Stretch (in case that matters).

Try installing node.js, and so, npm to latest stable version. Then, try the MM installer script again.

Worst case scenario, manually install MM.