I would say that 1/4" slop either direction on the pinion sounds a bit much to me, but I can't say the rear end is junk. The odds are it wasn't rebuild as stated and is just a standard tired 8.8.
The video I linked to original showed excessive play in hopes of giving you and idea what you want to avoid. With that said, just because your 8.8 doesn't have type of movement doesn't guarantee anything either way.
The best option at this point is to open up the rear cover, drain the fluid and take a look at what you have. Paying $150 for the setup isn't a bad price overall, the question is what will it take to make the rear end a good use-able setup?
The setup may have too much backlash, it could be bearings going out, it could be a rear end that is just flat worn out. Inspection is the only way to tell. If you plan on doing it yourself, then I recommend doing some research via Google and You Tube to see what you are getting into. Rebuilding an 8.8 is not extremely difficult, but good tools, precise measurement, and attention to detail will determine how successful you are and how long the 8.8 will last.
If you don't have the tools and equipment needed, Shop Press, Bearing/Race Driver Set, Torque Wrench both ft/lb and inch/lb, bearing pullers, and probably a few others then you might want to consider having it rebuilt professionally. Some of the tools can be rented at your local auto parts store, but not all of them. If you don't plan on rebuilding several rear ends over your lifetime then often the tools are not worth the cost of buying, therefore paying a Pro to rebuild the unit will be the cheaper and better option.
Good Luck!
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