There may be another issue here than a CPU bottleneck. For most games, the 6600k should not have an issue keeping the 1080 fed with data. Some games, such as BF1 are CPU heavy and those game will make use of the extra threads. But most games like really fast single core performance, which the 6600k has.
The 6600k is a great gaming CPU, so I would not say it is dead just yet as there may be another underlying issue. I would userbenchmark.com and see what it shows in the background of the CPU bench. As WildCard999 said, there may be a problem there.
I would go with the 7700k as an upgrade, if you need to upgrade. You will just need to update the bios and you can drop it in your current motherboard. There are some good prices right now for the 7700k too. As for Ryzen 5 or 7, unless you are using workstation type task, then there is no need. In most games, you will see lower fps in gaming with a Ryzen 5 or 7 over the 6600k.