Exactly Group IDs all seem to be negative numbers whereas individual user IDs (for one-to-one chat) are positive numbers.
It sounds like you got the right chat ID for your group. And since you were able to see the ACP Telegram IDs panel and type in the chat ID, you must have unzipped the extension into the right folder and got it enabled.
Unfortunately the ext doesn't have any logging right now so it's hard to say what the problem is
One thing is that if PHP's cURL support is not enabled, it will not send any messages (since the whole thing is basically coded using cURL). But I can't find a way to check that from the phpBB UI.
You could also try using the Chat ID of your personal Telegram account instead of a group chat. That way the bot will try to send private messages to you instead of sending them to the group. Personal chat IDs are positive numbers, here's one way to find out yours: https://stackoverflow.com/a/32777943
It would be good to add better diagnostics/logging to the extension anyway, but unfortunately I can't personally devote a lot of time to developing this ext, so updates will take some time.
EDIT: One more thing - Telegram bot auth tokens look like this: a bunch of decimal digits, then a colon (a ":" mark), then a random-looking mix of small and capital letters as well as digits. Did you remember to include both the part before the colon and the part after?