The only reason you would choose to use RequireJS for running your TypeScript program in a browser would be if you had hundreds of modules, but the page may only need two or three to perform its actions. We are talking serious big programs here, not lightweight apps or additional funky stuff for a web page.
Using RequireJS for a really big application means you only load the scripts you really need - not everything just in case.
For the sake of an example, imagine you wrote Microsoft Office as a TypeScript program, you could use RequireJS to load just the stuff you need as you need it. So at first, you'd load what you need for exploring files, then when a file was selected it would cause that module (maybe Word) to load, with its dependencies. This might mean you've downloaded only 10% of the program in several small chunks.
Module Loaders
TypeScript doesn't have its own module loader. It compiles TypeScript into JavaScript converting your module import statements into either CommonJS or AMD style code. Asynchronous Module Definition (AMD) is the module format used by RequireJS. CommonJS modules are used by NodeJS. You need to lean on these module loaders whether you are using TypeScript or JavaScript.
TypeScript simply transforms this:
import myModule = module('mymodule');
Into either require
or define
statements as per section 10.4 of the TypeScript Language Specification.