You will not be able to open those very large files with an MAT file extension using ACCESS (shouldn't such extensions be reserved?). They are POORLY named with this extension as MAT files - ACCESS Table shortcut file type - but in fact they are not. You are not even allowed to open them with NotePad or WordPad becuase they are so named.
Anyway I have opened all of the files downloaded at that site. They are not the files for the corpus itself, but a wordlist, files indicating text categories, and files for matrix data. The only thing useful is the wordlist, which you can get here: