Add this line at top:
declare const Buffer
and it should compile without errors.
Declarations is required to use node built in libraries or other global objects, you can manually declare it like above.
With new version of Typescript, you can also use official declaration files:
npm i -g typescript@next
npm i --save-dev @types/node
for other libraries, install @types/library_name.
more details: Improve Declaration File Acquisition, The Future of Declaration Files