If my opponent counters Deathgrip, do I still have to kill a friendly unit?

No, you do not have to kill a friendly unit if Deathgrip is countered.

According to Rule 425.1.a., a card that is countered is cleared from the chain and does nothing. Since killing a friendly unit is part of the effect (the instructions) of the spell rather than a cost, a countered Deathgrip is negated entirely and its instructions are never executed.

As established in the Core Rules (Section 425), countering a card prevents it from resolving, meaning the kill instruction—along with the subsequent Might bonus and the card draw—does not occur.