Some students might be running higher versions of Node than shown in the videos. In this case, some of the packages included in the starting files might be incompatible with your version of Node.
One way to fix this is to use a package called npm-check-updates to update the listed dependencies' versions inside the starting files.
https://www.npmjs.com/package/npm-check-updates
To use it, after unzipping and cd'ing into the project directory, but before running npm install
Run:
npm install -g npm-check-updates
Then:
ncu -u
Then:
npm install
Then:
npm start
Thanks to Ed and other students who pointed this out!