Does medical expenses that are not covered by your insurance but are paid with your HRA benefit card count as out of pocket expenses?

No. an HRA is an employer-funded arrangement.  the employer pays the bills up to whatever amount it has set. it has cost you nothing out-of-pocket.  however, any amount that was paid by you because it was in excess of what the employer paid would be a medical expense.   

If you have a flexible spending account (FSA), health savings account (HSA) or a health reimbursement arrangement (HRA), the funds in these accounts have essentially already been deducted, because they're contributed before taxes or reimbursed with tax-free money.

Your reimbursements from the HRA are nontaxable, and since you don't pay tax on them, you don't get a deduction.