I would not have used the electrical tape but that white tree guard is OK. Typically the most risky period for rabbits is the late fall to early spring. After that time you can take the wrap off for the growing season. 

Many do leave the wrap on for the whole year, but myself and other Extension services advise against it. The longer the wrap stays on the higher the risk for trunk girdling/abnormal growth. The risk might be even higher in your case due to the electrical tape being wrapped tight.

My recommendation is to keep the tree guard but ditch the tape. If you want extra protection that can last past the winter/early spring, putting up a cylinder of 1/4 inch hardware cloth that surrounds but does not touch/constrict the tree is a solid measure.

I would also consider using wood chip or some other biodegradable mulch instead of stones around the tree. There is good disagreement between arborists and other tree specialists, but I count myself firmly in the wood mulch camp as I believe soil health is important for tree growth.

Losing half of its diameter due to rabbit damage is very serious, but it isn't always a death sentence. You must also be vigilant and water/care for the tree as much as possible to give it the best chance to survive and to seal off the wound from the rabbit.

Best,

Shane