This is to supplement @JamesK's very clear answer. From the oscillations shown in Figure 1, one can estimate a period of the of the measured gravitational wave of about 5 milliseconds, which would correspond to an estimated frequency of the wave of about 200 Hz. Because the phenomenon is binary - a "wave" will come from each of the two objects, one can estimate the instantaneous orbital frequency at this moment to be half that, or about 100 Hz.
The discussion at the end of Section II mentions that in this case an orbital frequency reaching 75 Hz before contact could only be produced by two compact massive objects — black holes.
The annotations indicate an estimation from the figures only. An accurate analysis would require modeling the original data set.
From P. B. Abbott et al. PRL 116, 061102 (2016), section II and Figure 1:
To reach an orbital frequency of 75 Hz (half the gravitational-wave frequency) the objects must have been very close and very compact; equal Newtonian point masses orbiting at this frequency would be only ≃350 km apart. A pair of neutron stars, while compact, would not have the required
mass, while a black hole neutron star binary with the deduced chirp mass would have a very large total mass, and would thus merge at much lower frequency. This leaves black holes as the only known objects compact
enough to reach an orbital frequency of 75 Hz without contact. Furthermore, the decay of the waveform after it peaks is consistent with the damped oscillations of a black hole relaxing to a final stationary Kerr configuration.