The Google Drive API v2 to v3 migration guide says:
The exportLinks field has been removed from files. To export Google Documents, use the files.expor
I think you're placing too much emphasis on the word "method".
There is still a link to export a file, it's https://www.googleapis.com/drive/v3/files/fileIdxxxxx/export&mimeType=xxxxx/xxxxx. Make sure you URL encode the mime type.
Eg
https://www.googleapis.com/drive/v3/files/1fGBQ81haNU_nEiC5GITZD3bxT0ppL2LHg-C0ubD4Q_s/export?mimeType=text/csv&access_token=ya29.Gmo0BMvO-pVEPKsiD9j4D-NZVGE91MChRvwOcBSg3cTHt5uAClf-jFxcovQScbO2QQhwHS95eSGW1eQQcK5G1UQ6oI4BFEJJkntEBkgriZ14GbHuvpDL7LT2pKA--WiPuNoDDIuZMm5lWtlr
These links form part of the API, so the expectation is that you've written a client that sends authenticated requests, and deals with the response data. This explains why, if you simply paste the link into a browser without an access_token, it will fail. It also explains why the filename is export, ie. it isn't intended that your client would ever use a filename, but rather it should receive the data as a stream. This SO answer discusses the situation in more detail How to set name of file downloaded from browser?