External Payment API

I have a website for a business based in Belize. PayPal and Stripe aren't available for a lot of Belizeans based on banking restrictions, etc. There's a new app that allows Belizeans to accept international payments. It's called One Link Mobile and they use a web API to allow Belizeans to accept international payments on a website. The information they've provided with regard to the API is attached. My main question is whether or not it would be possible to use their API to securely accept payments at www.blackhawktourz.com? Initial research suggests this may not be possible based on a previous question found here:

Thanks in advance for any help/advice.

Chris