How to transfer the live photos to Mac via AirDrop? Before the update to High Sierra, when I received live photos via AirDrop, the system always asked I want to save them to the downloads folder or import it into the Photos app. When I choosing the second option, the imported live photos could then be exported as files to a disc, where for each live photo there were two files — an image and a short video.

After the update to High Sierra, the system immediately, without asking, saves the photos received through AirDrop into the downloads folder, with only JPG/HEIF files, without the live component video files.

How can I fix it?
This is not the fix but a workaround.

I exactly have the same issue with you. The interesting thing is that if someone send me Live Photos via AirDrop, (he is using iPhone 6), my laptop running High Sierra would give me the option to import via Photos app. But if I try to send live photos via AirDrop from my iPhone 7, I have no way of importing them directly into Photo app, and all I get is JPGs in download folder. I have been googling to see if anyone can offer solutions but so far, nothing except people are guessing as it is a bug...

But I really wanted to transfer my Live Photos wireless. And my solution was to use "Shared Albums" in iCloud. (I'm not sharing the album necessarily. Simply this is for me only.) I tested a few times and I see that Live Photos are intact under Shared Albums in Photo app on my laptop. Then I select them and import into Photo app. I can also add Live Photos from my laptop in the Shared Album, and I can grab them in my iPhone as well. 

Another cool thing about this is "A shared album can hold up to 5000 photos and videos. The photos and videos in your shared albums are kept in iCloud, but they don't count against your iCloud storage limit." Although for me, I'll keep the album empty after importing photos.

Here is more info on Shared Album from Apple website:
https://support.apple.com/en-us/HT202786

Till Apple can fix the bug, this is my workaround to import live photos on my iPhone without USB cable.