Shear forces are experienced by all molecules, and molecular complexes when they are treated roughly. So, for example, if you have a solution of high molecular weight DNA it will be very viscous, but if you treat it roughly by pipetting up and down through a narrow aperture the DNA strands will suffer shear forces strong enough to break covalent bonds and the solution will become less viscous.
Another example of the use of shear forces in biology is lysis of yeast cells using small glass beads. As the slurry of beads and cells is vortexes the cells experience intense shearing forces (forces tending to pull different parts of the cell in different directions) and they break open. They are not being physically ground by the beads.
In the specific case that you quote, you apparently have a multimolecular complex (MSL-DCC) held together by weak (non-covalent) interactions and interacting with the nucleosomes through a component called MSL-3. Without looking at the paper, it seems that this complex is prone to falling apart (during isolation?) as a result of shear forces strong enough to overcome the non-covalent binding interactions. Think of a helicopter with a man hanging on to the undercarriage with both hands. Then imagine a second man hanging on to the first man's boot lace with his thumb and finger. Who will fall off first due to the shearing forces experienced as they are buffeted by the wind?
The helicopter is the nucleosome, the first man is MSL-3 and the second man is the rest of the complex.
added later in response to MattDMo
looks from this that I was wrong - it's actually a French press and other homogenizers that generate shear forces. I don't think I made the glass bead story up, but I can't remember who told me. The BeadBeater people also refer to "cell cracking" not shear. Apologies everyone, I think the rest of the post still holds up, and thanks to MattDMo for the challenge.