Anything will conduct electricity with a large enough electric field. What distinguishes a semiconductor from a non-semiconductor in practice is how it conducts.
Silicon, $\rm TiO_2$, and many other materials conduct electricity by something resembling the free flow of electrons and/or holes (a.k.a. single-particle approximation). We can treat all these materials in a similar way, using similar equations, and we can call them all "semiconductors".
Other materials conduct electricity in other different ways, and therefore are not called semiconductors. For example, if you apply a small electric field to glass, current will flow via electron tunneling from one bound state to the next (Poole-Frenkel effect), which does not at all resemble the free flow of electrons and/or holes. If you apply a large electric field to glass, current will flow by the process we call "dielectric breakdown", involving motion of ions and defects etc., and which, again, has no resemblance whatsoever to the free flow of electrons and/or holes.
I like this operational definition because it explains otherwise-inexplicable terms like how doped diamond is called "semiconducting diamond". You might think, diamond is either a semiconductor or it's not, so how can you describe a certain type of diamond as being "semiconducting diamond"? Well, because when it's appropriately doped, it conducts current by something resembling the motion of free electrons or holes, and when it's not appropriately doped, it conducts current by Poole-Frenkel effect, dielectric breakdown, or whatever.
It's a general rule that as the bandgap increases, the material becomes more and more ionic, and the electrons and holes look less and less like free particles and more and more like polarons. It's also a general rule that as the bandgap increases, would-be dopants are less and less likely to be able to ionize to create "free" carriers (they tend to create levels deep in the bandgap). Therefore, as bandgap increases, it's less and less likely that you'll find anything that should be called a semiconductor.
But there's no hard boundary. Even aluminum nitride $(6.2\ \rm eV)$ and diamond $(5.5\ \rm eV)$ can behave as semiconductors---in special, carefully-controlled situations.
$\rm TiO_2$ is very much a typical semiconductor, as far as I know. It differs from silicon, $\rm GaAs$, etc., mainly in that it's impossible to make it intrinsic $\rm TiO_2$ or p-type $\rm TiO_2$ (well, some would argue it's merely "almost impossible"). But if you keep that in mind, the equations you cite should still apply.