I don't believe it is using any type system described outside of the TypeScript compiler. The goal of the system is to accurately describe real-world JavaScript programs and semantics, not to introduce a formalization that existed elsewhere and impose it on JS.

As a consequence, it has aspects of structural types, dependent types, type narrowing, and myriad other features that exist solely to model real-world JavaScript.

As far as soundness: it's not a goal of the type system. https://www.typescriptlang.org/docs/handbook/type-compatibil...