No. TypeScript has no dependency on classes the way Java or C# does; nor is class-oriented code the recondeded style by the TS team. As a matter of fact the typescript compiler core is all written as functions and immmutable objects with no classes (except for a polyfill for Map and Set).
TypeScript 2.3 has support for vue.js this injection style patterns (see https://github.com/Microsoft/TypeScript/pull/14141) which are way out of the realm of class-centric programming languages. Similarly the inference cabalities (expanded in 2.4) and the fundamental nature of the type system being structural rather than nominal is another give away of the language nature and direction.
So the short answer is TypeScript is a superset of JavaScript; and is as class-centric as JavaScript is.
TypeScript 2.3 has support for vue.js this injection style patterns (see https://github.com/Microsoft/TypeScript/pull/14141) which are way out of the realm of class-centric programming languages. Similarly the inference cabalities (expanded in 2.4) and the fundamental nature of the type system being structural rather than nominal is another give away of the language nature and direction.
So the short answer is TypeScript is a superset of JavaScript; and is as class-centric as JavaScript is.