This is an interesting and nontrivial question. It is actually considered in some detail in the original paper, which your cited source links to: Ahn et al Phys Rev Lett 121, 033603 (2018). Many readers will not have access to that paper, but it is also mentioned in the Physics Focus article which is available to all. The structure of these particles is two nanospheres of silica, which overlap somewhat, so the strength is determined by the silica bonds in the relatively small overlap region of the structure. If you try and pull the dumbbell apart, it's not just the force that matters here, but more like the force per unit area in this region.
Edit: it's worth mentioning that, when you consider the mechanism of fracture of solids, it isn't just a question of adding up the bond strengths. In crystals, fracture is strongly affected by the response of defects in the structure to the applied stress; in amorphous materials, such as these, the defects are not so crucial, but it is still not just a back-of-the-envelope calculation.
Basically, they state that
The ultimate rotating frequency is determined by the ultimate tensile
strength (UTS) of the material.
They estimate (by finite-element computations) the maximum stress, for a typical dumbbell geometry and rotation rate, as 13 GPa (13 Giga-Pascals) which they point out is two orders of magnitude greater than the ultimate tensile strength for a bulk glass (amorphous silica). They actually have a nice picture of the stress distribution throughout the dumbbell, modelled in this way: almost everywhere in the two spheres, it is down in the range 0.1-1.0 GPa, but in the crucial junction between the spheres it jumps up to 13 GPa. They compare the strength of their dumbbells to that of
state-of-the-art silica nanowires
which has been measured Nano Lett 9, 831 (2009) at 10-20 GPa (with a theoretical upper limit of $\sim$ 30GPa) by simply pulling them until they break.
So the bottom line seems to be that such strengths are achievable in nanoscale materials, and are much higher than we are used to in comparable bulk materials; but that the reported rotation speeds are indeed quite close to the limit that would be expected to cause these particles to disintegrate by centrifugal stress.