My Photo Stream does not transfer any video, only still frames. The live part of your Live Photo is a video component, so My Photo Stream will only transfer the high resolution still frame of the Live Photos. see: My Photo Stream - Apple Support
Photo formats that you can use with My Photo Stream. My Photo Stream supports JPEG, TIFF, PNG, and most RAW photo formats. My Photo Stream doesn't support video or Live Photos.
To transfer your your Live Photos alive, delete the still frames from your Mac, that you already imported from your iPhone with My Photos Stream, disable My Photo Stream and empty the Recently Deleted Album in Photos. Now connect the iPhone with a cable directly to your Mac and import the missing items - any videos you have taken, the Live Photos or Portrait Mode photos. Import photos from a camera or phone using Photos on Mac - Apple Support
If you are taking Live Photos and videos on your iPhone, you may want to stop using My Photo Stream, because it will just complicate the import from your iPhone. Import the items directly or switch to iCloud Photos.
iCloud Photos is the easiest way to transfer the photos and all adjustments you applied on the iPhone.
Use iCloud Photos to store photos in iCloud - Apple Support
