He's not writing the C++ standard library from scratch. He's writing his own library, in a different namespace, with some similar functionality. It's easy to write a non-standard library that only satisfies your limited subset of needs. People do it all the time. It's not special.

The ABI stability boast is based on having no legacy to support. It will work fine as long as everything is shipped only as code and the whole world needs to be rebuilt from scratch every time and even then, you never change any code ever even for a major bugfix. That's hardly practical in the real world where one tiny misstep on the ABI front can result in billion-dollar multinationals threatening suit (ask me how I know). It's a facile claim.

The C++ standard library hasn't been known as "the STL" for almost 30 years, ever since part of the STL was modified and adopted into the C++ standard library. Most of the features he's providing implementations for were never a part of the STL (file I/O, strings, hash maps, UTF-8).

I maintain an implementation of the C++ standard library for a living. It's a full-time job. It's a huge library (note to the committee: please stop) and it's really easy to mess something up. But if you want to write your own library that doesn't do what the standard library does or meet any of its requirements and implementation constraints or serve its real-world purpose, go right ahead. Just don't claim you're writing your own C++ standard library. You're not.