There are dozens of loyalty point systems on Twitch, and the majority of them work by polling the undocumented chatters endpiont tmi.twitch.tv/group/user/<Channel Name>/chatters and awards points to those who are in the channel. Keep in mind though that this is a list is of users that are currently logged in to chat, and not a list of those who are actually watching the stream. You will not have access to the VHS API/Drops, so the chatters endpoint is your main option.
The loyalty point systems that already exist generally require a streamer to go to their site and connect with their Twitch account, and then the service will start polling the chatters endpoint (interval, and polling when offline or online only varies depending on service). Some services also require individual users to connect to the site before their points start adding up.
From there, it’s entirely up to you how you plan to go about recording the data (as long as you follow Twitch’s developer agreement on data storage that is), displaying user points (some use bot commands, others through their site, some are starting to use Twitch Extensions), and issuing rewards.