It was my understanding that use Babel allows you to use ecma6 javascript in an ecma5 environment by transpiling. When I use 'import' however, the 'import' is transpilied to 'require'. 'require' isn't ecma5 and requires the library 'require.js'. Therefore you can't use 'import/ export' without additional dependencies, is this correct?
Yes, Babel is just intended for translating new language features to be compatible with modern javascript engines. Babel doesn't compile to require.js module import syntax. Rather it uses the CommonJS module syntax as used by Node.js. So you could run the code directly without further build dependencies in Node.js.
As it operates on single files at a time and is a straight forward translation, it doesn't make any decisions as to how you want to include the source code of those other files into the current one.
That said, if you are going to use it in browser, you will need a build system or bundler that supports CommonJS modules statements: