  Astrophysical sources outside the Milky Way, such as active galactic nuclei
and star-forming galaxies, leave their imprint on the gamma-ray sky as nearly
isotropic emission referred to as the Extragalactic Gamma-Ray Background (EGB).
While the brightest of these sources may be individually resolved, their
fainter counterparts contribute diffusely. In this work, we use a
recently-developed analysis method, called the Non-Poissonian Template Fit, on
up to 93 months of publicly-available data from the Fermi Large Area Telescope
to determine the properties of the point sources that comprise the EGB. This
analysis takes advantage of photon-count statistics to probe the aggregate
properties of these source populations below the sensitivity threshold of
published catalogs. We measure the source-count distributions and point-source
intensities, as a function of energy, from 2 GeV to 2 TeV. We find that the EGB
is dominated by point sources, likely blazars, in all seven energy sub-bins
considered. These results have implications for the interpretation of IceCube's
PeV neutrinos, which may originate from sources that contribute to the
non-blazar component of the EGB. Additionally, we comment on implications for
future TeV observatories such as the Cherenkov Telescope Array. We provide sky
maps showing locations most likely to contain these new sources at both low (<
50 GeV) and high (> 50 GeV) energies for use in future observations and
cross-correlation studies.
