If I recall correctly, when serverbot is active, it just outputs additional cvars for public query. In this case I'd go like this:
1. Make an API script that will query the gameserver, retrieve and parse infos (think zPAM packs the array in a simple way so explode() should do the trick) and output the content in some notation. Also can take a look at this library to understand how to send queries to your gameserver: https://github.com/Austinb/GameQ
2. Query your API script with AJAX.
3. Play around with JS and frontend.
4. Put it in a loop.
In case you want to do this for website which will have bigger traffic, it might be a good idea to make a daemon script on your server which will automatically query gameserver once let's say every 30 seconds and store the results in a database (might need some playing around with locks though). Then make a public API script which will read these results from database and output them back to the client.
Otherwise you're risking having 100 people on the website and all of them constantly requesting your script to send 100 queries to the gameserver which will no doubt result in gameserver lags / your server being banned from gameserver's ISP / similar inconveniences..