I tried reinstalling node.js a few times, and tried with different versions, and I still get the same error. I'm also running the CMD as administrator. It seems like it doesn't find json-schema, I even tried to install it manually, but same error appears. Here's the error message I get:
C:\> npm install -g @angular/cli
npm WARN optional SKIPPING OPTIONAL DEPENDENCY: fsevents@1.1.3 (node_modules\@angular\cli\node_modules\fsevents):
npm WARN optional SKIPPING OPTIONAL DEPENDENCY: Error: EPERM: operation not permitted, rename 'C:\Users\admin\AppData\Roaming\npm\node_modules\.staging\fsevents-edb66af1\node_modules\asn1' -> 'C:\Users\admin\AppData\Roaming\npm\node_modules\.staging\asn1-98b68b78'
npm ERR! path C:\Users\admin\AppData\Roaming\npm\node_modules\@angular\cli\node_modules\@ngtools\json-schema
npm ERR! code ENOENT
npm ERR! errno -4058
npm ERR! syscall rename
npm ERR! enoent ENOENT: no such file or directory, rename 'C:\Users\admin\AppData\Roaming\npm\node_modules\@angular\cli\node_modules\@ngtools\json-schema' -> 'C:\Users\admin\AppData\Roaming\npm\node_modules\@angular\cli\node_modules\@ngtools\.json-schema.DELETE'
npm ERR! enoent This is related to npm not being able to find a file.
npm ERR! enoent
npm ERR! A complete log of this run can be found in:
npm ERR! C:\Users\admin\AppData\Roaming\npm-cache\_logs\2018-03-15T07_42_19_026Z-debug.log