Are old Humble Bundle gift links still working?

Yes

Old HB that use it still work.

just generate the gift links and give it to the winners, it works fine
for more information, after the winners claim the gift, they will obtain a CD key to redeem in steam client, the "click to redeem" method is gone, as you've know so far

I activate old HB link for Mafia II few day ago and it works fine.

Thanks!