On some hosting environments (HostGator, GoDaddy) there is an issue with the resources dedicated to a single instance of Shared Hosting. While trying to prevent a single instance to compromise others in Shared Hosting environment, they set the limits too low. Especially limits related to memory and processing power.
As a first step, please try to set Server Recommended Settings and try the import again.
If that does not work, most probably the hosting limit prevents creation of thumbnails for images larger than 60-70k.
The consequence is that you will not be able to see the thumbnails in your Media Library although the images are there (thumbnail was not created) and you will not get optimized images for different elements on the site. You will get the original ones which are usually not optimized for the placeholder they have been put in.
In order to import the demo in such environment, you need to repeat it over and over again. The import is incremental process and eventually it will finish (it usually takes 30 or more retries since it will crash on the import of each image larger than 60kb). You can check the progress by refreshing Media Library window – each retry should add one or more images (the ones with 60kb and more will be grey while the smaller ones will have a proper thumbnail).
Once the import finishes you will have a functioning demo, but we strongly recommend to resolve the resources issue with the hosting or change it since it will almost certainly create other problems in the future.