So, this is what I do for a living. The truth about Quartz countertops is that they do scratch and chip(although that is something that happened during fabrication and/or transportation). He probably used an inexpensive off brand of quartz - and he is not a licensed fabricator so, unfortunately, you probably got what you paid for. They are not heat or scratch proof - only resistant, regardless of brand.
Your recourse is that he installed it scratched and chipped and should replace it with undamaged material. Unfortunately, again, he is unlicensed which probably means you don't have much leverage. If you can withhold a portion of payment until he has completed the project - then talk with him about the damaged material. If he wants to continue to do business with you he will work with you on a discount or replacement.
This would be one of those lessons we learn and pay for in the process of Real Estate investment. Using licensed contractors gives you much more leverage to make sure work is done right.