There are two reviews of that cooler on newegg.
both terrible.
I suppose since he already bought it, you could install it and run.
I would return it unopened.
But, what a waste for a really nice processor like the 8600K!!
Best to ask for opinions BEFORE you buy.
What is the make/model of the case?
What will you need to put inside?
If you have 145mm available, the cryorig H7 will fit.
Low profile downdraft coolers are not very efficient.
You may be needing to look at a liquid cooler if your case is really small.
I might also point out that if you do not overclock a 8600K, you are leaving some 30% performance on the table.