Yep, thats a torn diff bushing. Once its torn, it needs to be replaced. Myself and another member did the whiteline replacement on my car and wrote up a DIY, its in the DIY section somewhere. Its not that bad of a job.
Edit: Found it
DIY: Whiteline rear differential bushings
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2010 Nissan 370Z 40th Anniversary Edition #762/1000
| Forgestar | Michelin | Swift | TRS | Z Speed | ARK | Z1 | Hawk | CFE | Evo-R | GTMat | Stillen | Seibon | Whiteline | Pioneer |