  In the context of whether a massive compact object recently observed in the
GW190814 event is a neutron star (NS) or not, we have studied the role of the
parameters $\kappa$ and $\Lambda_c$ of the Eddington-inspired Born-Infeld
(EiBI) gravity theory on the NS mass-radius relation, moment of inertia, and
tidal deformability. The results are compared to recent observation constraints
extracted from the analysis of NS observation data. The NS core equation of
state (EoS) is calculated using the relativistic mean-field model with the G3
parameter set. In the hyperon sector, the SU(3) and hyperon potential depths
are used to determine the hyperon coupling constants. For the inner and outer
crusts, we use the crust EoS from Miyatsu et al. (2013). We also maintain the
sound speed to not exceed $c$/$\sqrt{3}$ at high densities. We have found that,
in general, the NS mass significantly depends on the value of $\kappa$, and the
radius $R$ is sensitive to the value of $\Lambda_c$. Moreover, as $\Lambda_c$
is equal to zero or less than the accepted bound of the cosmological constant,
the NS within the EiBI theory is compatible with observation constraints,
including $2.0 M_\odot$ mass, canonical radius $R_{1.4 M_{\odot}}$, moment of
inertia, and tidal deformation. Our investigation also reveals that the $2.6
M_\odot$ mass compact object and current observational constraint of canonical
radius $R_{1.4 M_{\odot}}$ can simultaneously be satisfied only when the
$\Lambda_c$ value is unphysically too large and negative. Therefore, within the
spesific EoS employed in this work, we conclude that the secondary object with
$2.6 M_\odot$ observed in the GW190814 event is not likely a static (or a
slow-rotating) NS within the EiBI gravity theory.
