Why it runs on your machine
Most online video tools upload your clip to their server, process it there, and send it back. These don't. Your browser has video encoders built in, the same ones that power video calls, and these pages use them directly. A 500 MB clip doesn't have to go anywhere, so there's no upload to wait for.
Tools run in your browser, so a laptop takes longer than a gaming PC, and the page has to stay open. How it works covers what the page can and can't do.