Theoretically, gravity in $n$ dimensions is described by the Einstein-Hilbert action:
$$
S\sim\int\mathrm d^nx\sqrt{-g}\ R
$$
However in pure 3D gravity, there are no propagating gravitational degrees of freedom. This is because the Weyl tensor is identically zero, and since it encodes the behaviour of gravitational waves, it is clear that gravitational information cannot propagate across the manifold. The Weyl tensor also contains the information about the Newtonian potential and higher-order potentials, so surprisingly in 3D gravity, masses do not attract! As a result it was actually thought for a long time that the theory was trivial - that is, until the discovery of the BTZ black hole in 1992. Furthermore, 3D gravity with $\Lambda<0$ also shows features like spinning particles, which appear as local conical defects, as well asymptotic symmetries of spacetime.
However, recall that the independent components of the Riemann tensor (the "field strength") can be decomposed into to the Weyl tensor and the Ricci tensor, the latter describing the curvature due to matter distribution ("sources"), which is non-zero in general. So 3D gravity is not trivial as you seem to think.
Whether or not one wishes to deem a theory with features like this as "gravitational" is obviously a purely semantic choice, but theorists like 3D quantum gravity for multiple reasons:
The famous AdS/CFT correspondence is a duality between a gravitational theory in $n$ dimensions and a specific quantum theory in $n-1$ dimensions, and provides non-perturbative results in string theory. The original discovery was apropos AdS5/CFT4 by Maldacena, however analogues have been found in other dimensions. An AdS spacetime is one with a constant negative cosmological constant, and the first benefit in 3D is that any spacetime with negative curvature is locally equivalent to the AdS spacetime. One might think to simplify further to AdS2, but this is in some regards too trivial: AdS3 provides the right balance between complexity and tractability. As I mentioned, 3D gravity has rotating black hole solutions that asymptote to AdS3, and its partner CFT2 is sufficiently well-understood that one can translate results between the two in order to provide insights on solving the information loss paradox, aid in microscopic black hole entropy computations, etc. AdS3 is also amenable to serve as a background for WZW-models of string propagation. As such, 3D quantum gravity is heavily entwined with string theory - in fact, it is not even known whether there us a well-defined description of it without embedding it in string theory.
An important theoretical endeavour is to describe the gravitational force as a quantum theory and incorporate it into our current descriptions of the other forces to form a theory of everything. This is incredibly difficult, so analysing the more tractable 3D quantum gravity is a good way to seek hints, extrapolate results and develop the requisite tools. Note that pure 3D gravity is not the only option here: one is free to couple Chern-Simons/topological terms in order to produce gravitons.
While 3D quantum gravity is naïvely non-renormalisable and looks doomed as a quantum theory, the techniques mentioned above enable us to gain insights about non-perturbative formulations and features of such a quantum theory. A good deal of progress in this regard came from the Chern-Simons formulation of 3D gravity, a construction due to Achúcarro, Townsend and Witten: I highly recommend Witten's paper for a good review of the modern methods and results.
