Shin Karate [or New Karate] is the name of the format. Its open to all Karate styles [much like Karate Combat is] it was originally known as K-2 since it was a feeder system for K-1 to give Karate fighters a chance to fight and gain experience under K-1 rules before jumping into K-1. Hence why you saw Nicolas Pettas in that video [along with Glaube Feitosa in a traditional Knockdown rules match] When K-1 collapsed it rebranded itself to Shin Karate [or New Karate since Shin means New or True in Japanese] and still holds events.
Here's the link to their site .
http://www.shinkarate.net/
and Youtube page
https://www.youtube.com/user/shinkaratek2k3k4
Not quite true.
Shinkarate had a deal with old k-1 to use the name k-2 etc, but they are not related as organization.
They always called themselves shinkarate and are actually older than k-1 shinkarate was founded 1985, k-1 was founded 1993. Back then there was no connection between the two. The cooperation didnt start until early 2k.
Their rule system are still called K2,K3,K4 and K5 (basically, K2 is full rules, the following rule-systems adding progressively more protection, rookies -k3, youth-k4 and toddlers in marshmallow suits -k5). It was strictly amateur, and the pro fighters was sent into kickboxing -which for years meant k-1 due to the deal they had. Masaaki Noiri was one.
I dont know how they do currently, if they still are strictly amateur, sending their pro level fighters to other kickboxing organizations . I see that they have started a k-2 GP.
I assume they still have some kind of deal with the japanese k-1 (there is still such a thing, although it is not comparable with the old one). Shinkarate DID briefly rename their rulesystems from k2-5 to Q2-5. But it was only temporary.
Several of the top japanese names from the last years of K-1 glorydays, came from Shinkarate, and many famous kickboxing gyms in japan are (or was, Im not up to date) connected to them.
There is an official shinkarate style too, but you do not have to train it in order to fight in its tournaments, and your gym does not have to teach it to be a member of the shinkarate organization. Its kind of an optional extra.
The rules in shinkarate are glove karate. Basically it is slightly modified kyokushin rules. with boxinggloves and punches to the head allowed.