I have the following task:
<input type=file />
No, sorry. You can't access any of the file data until it's uploaded to the server, which is certainly what the library you linked to does. Once the file is uploaded, you can save it somewhere, re-download it and read EXIF data from it.
The above answer used to be correct, but most modern browsers now allow file access via the js file apis. Feel free to use that, but you should also use a server-side solution if cross-browser support is required.