If you run into this issue, read this page: https://www.bramvandenbulcke.be/en/kb/failed-node-sass3131-postinstall-script
The solution in my case:
1) Delete the package-lock.json file
2) npm install gulp-sass --save-dev
3) npm install node-sass@latest
Version specific notes:
node-sass@3.13.1 runs only on versions of Node.js up to v7 as stated in the release notes: