I quickly went through the web page. You will need to install the library on your server. If you have a VPS with terminal access, it should not be a problem. Otherwise, you need to ask the server support to install it.
Then the bit of code that should be pasted on the page can take place in a page source.
A web app has no access to the client hardware. So your web app can not print to a specific printer without a dialogue. You need a local service or a server app to handle this.
Interesting blog article how to write a local background service to handle that problem with POS printers:
It would not be too difficult to have a small web service app running on the client machine that takes documents to print, and sends them to the POS printer.
I would create my own specialized “browser” for that. And such specialized client would talk to the server, find a receipt to print, download the data, and send it formatted to the printer.