In that example, you're using /1/files to access file data. In API v2, the replacement is /2/files/download:
https://www.dropbox.com/developers/documentation/http/documentation#files-download
That's a "content-download endpoint", so the standard way of using that is via a POST with 'Authorization' and 'Dropbox-API-Arg' headers. To just use a GET with it instead though, i.e., so you can just use a URL by itself, you can use the URL parameters documented here:
https://www.dropbox.com/developers/documentation/http/documentation#formats
So, to access a file at "/bbbb/aaa.xlsx" the API call parameters for /2/files/download would be:
{"path": "/bbbb/aaa.xlsx"}
URL encoding those for use with the `arg` URL parameter, along with the 'authorization' URL parameter, the result would be:
https://content.dropboxapi.com/2/files/download?authorization=Bearer%20ACCESS_TOKEN&arg=%7B%22path%22%3A%20%22%2Fbbbb%2Faaa.xlsx%22%7D
Be sure to replace ACCESS_TOKEN with the actual access token.