thanks for testing this, and for the link!
Unfortunately, I have bad news: Your file is just too big for TablePress.
Although there's no direct limit in theory, a table of this size is too much for the memory (and then also the user interface) to handle.
Even if we were successful in importing this file, you would not have fun with this table. Basically, the "Edit" screen of TablePress would be virtually unusable for this table, due to the large amount of input fields. Also, the rest of the site would probably be slow, as the table would always be loaded entirely.
For a table like this, which is more like a large database, a custom database solution, e.g. based directly on mySQL and PHP will be the much better option.
If you want, you can then also add the advanced features like sorting, search, and pagination, by manually using the DataTables JS library from http://www.datatables.net
I'm really sorry that I don't have better news or a working solution here :-(