Unless I completely missed some aspects, it mostly just seems like an interface to their database. While this is great for some advanced workflows, the vast majority of use cases are all very similar: "create subscription and customer", "change subscription", etc. Common workflows require quite some coding, and there's no support for transactions! IMO a good API design should be more thoughtful than providing an interface to your database.
I don't think the documentation is especially well written, although it's not bad either. What's worse is that the stripe API docs hijacks my CTRL+F key so using my browser search is a massive PITA. This is such a fucking annoying fucking thing that I'll break my "don't say fuck on discussion forums"-rule for this. I fucking hate it. I tried disabling JS but that results in every navigation doing a full page refresh which easily takes over 5 seconds.
Also, browsing the docs isn't super slow or anything, but it's also not quite fast enough to feel "natural".
The checkout docs actually are pretty meh. Much of it is written in "tutorial" form and unclear on details.
As for the site design ... it often takes >5 seconds to load anything after clicking and it easily uses more than 100M of memory per tab. I recently wanted to load a bunch of customers so I opened them in about 10 different and my entire laptop just ground to a halt. I've actually been procrastinating on some Stripe stuff I need to do for the last week because I dislike using the UI so much.
Is it all absolutely terrible? No; it's passable, I guess. But do I share any of the enthusiasm in this article? Not even close.