The paper is way over my head, but it seems to be an important result in the field of finite geometry, i.e. linear algebra over finite fields. Finite geometry often provides the mathematical foundations for error-correcting coding schemes that are found in many applications where information needs to be transferred efficiently and robustly. So, I could guess that this result would have practical applications in at least that ___domain. However, since that ___domain is so important (e.g. packet transfer underlying the internet), this could be a very important paper indeed, even for "real-world" applications.