Triangle K is one of many organizations that supervise kosher food prep. To provide truly kosher food, you need a constantly supervised kitchen. In my experience, it's not possible to run kosher and non kosher on the same premises. (But since the supermarket deli does it, then there must be a lenient org. that allows it).
Kosher style is in demand a lot these days, with so few places offering kosher. Also, to keep a place kosher obviously costs money, which a lot of customers aren't willing to absorb. I think that kosher style is great to offer for larger events, like weddings and Bar Mitzvahs. For a family that wants kosher, it's because they keep a kosher home, and kosher style won't cut it. What I'm saying is that for retail, kosher style doesn't make sense, but for wholesale, it does. And all that kosher style means, is no dairy with a meat meal. My humble opinion.