Certified GKH Gardening Expert
These roots will send adventitious shoots out on occasion. They will seek any area that is suitable for them to send a shoot, and gaps in concrete are perfect for this.
Sealing those areas off, and maintaining some of the cracks will eliminate most of this, outside of hand-pulling and chemical control.
The good news is that these are not very destructive, however they are taking advantage of a place to send a shoot. Being a Chinese Holly, these will be more prolific than our own native types.