The values are indeed saved locally on your (user's) device. The game client is also downloaded locally on each user's PC, and run using the capabilities of each user's system, even though they got it from a website.
You'll need some way to communicate the data of interest to your server PC, and a way to get data from the server. A common way to do this with a web server is through AJAX, PHP, and MySQL.
Another way to do it (probably not what you're looking for) is to have peers connect and communicate directly with each other (through a host), through something like the multiplayer plugin. However data normally isn't persistent with this method either, unless you have a way to keep a dedicated host up. The dedicated host would handle storing, retrieving, and syncing data with connected peers.