Can taxpayer offset Prize money from a form 1099 Misc with gambling losses

Nope

If the "prize" was from gambling, yes, the losses would be deductible on Schedule A.

Otherwise, no.

But the fact the business that issued the 1099 calls it a "prize" makes it very questionable if it was gambling.

I had a client who spent hundreds in postage every year entering sweepstakes.  He would occasionally win a toaster.  Oh, maybe that was for opening a bank account. I once had a client who had 11 IRA's and 11 toasters.  But that's not the question.  We deducted the postage as a miscellaneous deduction.  Then they limited it with the 2% haircut.  Then they suspended it altogether.  

But what you have is not gambling, or it would have been reported on a W-2G.

I have made an offset to the "suggested retail price" of a prize won. e.g. Refrigerator with a MFSRP of $1,000 that I can produce an ad showing it on sale at $800, then I report the $1,000 with another "other income" of "adjustment to 1099-MISC" actual value of a -$200.