What can I do if someone doesn't respond after asking their permission for a giveaway deletion?

You are just gonna have to take the L, try not gifting keys if you are unsure if they work, cheers

Actually they don't have to agree with deletion of the giveaway. It is seen as the polite thing to do on this site, but nobody is obliged to do it. There are several groups, which have this as their main setup rule, you might wanna give keys you're uncertain about there.
In this particular case you might have to live with a not received mark on your profile. It happens... Anther solution could be to seek out a trade for a working key. Shouldn't be that difficult, game has been bundled. Sites to look for trades are Steamtrades and barter.vg.

Good luck!

Well, do nothing. You don't have to delete giveaway. If key is not working - it does not matter, if he will mark it as not received, if he will keep in not marked at all, or if you will be able to delete it - you gaining nothing and losing nothing. Well, except that in case of deletion you will waste time of moderators, so actually it will harm other users (without any benefit for you). Unless you plan to buy a new key for the winner - just forget about this giveaway.

there are some groups for unsure keys ,but i usually avoid it .
Overall you have 3 outcomes.
He will let you delete the giveaway someday.
You buy another copy of the game gifting it .(its pretty cheap on keyseller sites.
Or you will have a not received on your profile .

It looks like they wrote a steam review in Russian, so maybe they don't speak English and are just ignoring your messages for some reason. You could try using google translate and converting a message to Russian and posting that on the giveaway. I would try to use simple words and sentences so the translation works better.

Either that or just wait for them to mark it not received. It's not a big deal to have a not received on your account.

Thank you each and every one who answered. Good info!