If I have a grandchild who is not my dependent and for whom I do not provide more than 50% of their support, can I still deduct directly paid medical expenses?

Unfortunately, no. You can deduct medical expenses for yourself, your spouse, and your dependents. Only.
 Your payments would be considered a gift to the child, and a gift to a specific person is not deductible as a charitable contribution.
If you paid more than $14,000 as a gift to the child, then you may have to file a Gift Tax return,
Form 706, Gift Tax
http://apps.irs.gov/app/picklist/list/formsPublications.html?value=706&criteria=formNumber&submitSearch=Find

Turbotax does not support Form 706, so you have to do that by hand.
Usually, you do not actually have to pay a tax, what happens is that your lifetime exclusion for estate tax purposes is reduced.

If you directly paid the medical institution, no Gift Tax return would be required.

Although there is a such thing as a "medical dependent", because the parents are claiming him, I don't think you would qualify for that.

It's possible that the payment could be considered a gift to the parents.  In that case, his parents would be able to claim the medical deduction.

I concur, that the medical payments are a gift to the parents and they are able to claim the medical deduction.

I presume the gift and subsequent expense deduction is for medical expenses only and dose not include the premiums paid for that coverage, correct?  Thx

It depends on how you paid the premiums.  If you paid the insurance company directly, it does not qualify as a gift, but it doesn't qualify to be deducted as medical expenses either if the covered person is not part of your tax family.  If you "reimbursed" the person, the amount counts as a gift and the exclusion amount for 2022 is $16,000.

@Johnpat