the stripes on your cooler is preapplied thermal paste, i have a corsair gtx h100i with my 6700k, the paste is good quality no need to apply more.
Yep, that grayish material is pre-applied paste, and you can mount it as is (removing any protective films of course). I wouldn't call it the "modern form", but some coolers just come with it pre-applied.
To answer your other question: Yes, thermal paste is necessary. If you decide to get an aftermarket cooler one day, you're going to want to apply some if it's not there already.
Many thanks to both of you. Good night from Berlin
Just FYI - By now I have installed my new CPU and am very happy with it. Thanks again for giving me the trust re. the preapplied thermal paste.
The only thing I had not considered is that I now have to buy me a new Win 10 licence (new motherboard) ;-(