Is there any way to contact another user other than posting a message in their giveaway?

Besides Steam there is not much you can do and nothing you must do beyond what you have already provided.

You can only see the email if they win one one your giveaways. If you are the winner you can only message someone through the giveaway page or Steam.

Just had a look, and this game isn't even available on Steam anymore (I suspect it's been removed by Valve themselves), so it may be possible all keys for the game have been revoked also. The person who did the giveaway has three other games with the same "key already activated" issue by the looks of it, so I would guess you're unlikely to see any resolution in your favour.

you win my giveaway, confirm her