In that case, there are other possibilities. I know Google play support IAP and I assume others like the Microsoft store does. But, you're talking about pure web based games so, here's one option.
PayPal, and I assume others, have what's called and Instant Payment Notification. The way the IPN works is, the customer clicks on the PayPal button and it takes them to the PayPal site to make the purchase. Once that transaction is complete, PayPal contacts a URL that you designate. In my case, I have it contact a PHP script. With the data that PayPal sends, I generate registration keys for some software that I sell and then, add all that data to a MySQL database.
Google also offers something like this with Google Pay
So essentially, there are payment methods out there that you can customize to do pretty much whatever you want, it just takes the skills to make the back end work.
As for locking into one particular payment method, I disagree. One of the axioms of the internet is that nothing lasts forever. The minute you lock yourself into one provider or source, your success is bound by their success. The minute they fail, so do you.