My guess: most likely through these exchange's APIs, which is publicly available for every user(as far as I know).
That's exactly right. It's explained in their FAQ here:
https://mcafeemagic.com/faq.phpQ: How do I connect my API's to start trading?
A: After you get API from your exchange, on the Magic dashboard click the exchange, then the + button, enter your API and save. Magic will verify if your key is valid.
APIs are freely available to all users. All this site is doing is providing a platform to import all your APIs to at once. It offers nothing which you can't do yourself, but it is charging $1,000 a year for the privilege.
I wonder what kind of “magic” does he have for us in using his crypto trading platform?
The only "magic" here is that some users are crazy enough to pay $1,000 for something they can access for free.