is the Corsair - H80i v2 70.7 CFM Liquid CPU Cooler good enough to cool it while gaming?
Honestly the i7 8700k needs a lot of cooling, anybody who says otherwise doesn't have one or hasn't done their research properly. So I do recommend water cooling even if you aren't overclocking. The be quiet dark rock 3 is a beast air cooler but I don't know if it is enough to cool it, and no the H80i isn't enough. You would want a 240 mm radiator atleast.
I have an 8700k and I overclock it with a cryorig h5 ultimate air cooler and I got it to 5.1 ghz with fine temps
What are fine temps for you?
I can recommend Corsair - H115i 104.7 CFM Liquid CPU Cooler which is a bit pricey but since you are running an 8700k, sounds like you are going all out. If you need some cheaper options, I can recommend but at a cost for performance. This should cool VERY efficiently, also if you want something more visually pleasing then I recommend the NZXT's Kraken. More specifically the Kraken X62 Rev 2
Ignore everyone in this forum YOU DO NOT NEED A WATERCOOLER.
Unless you do a custom loop then water cooling is not worth it. A high quality air cooler will out perform an AIO most of the time. It depends on the cooler of course. I just advise getting a high quality air cooler. There are pros and cons to both but there are a lot more cons on the water cooling side. For example on an air cooler the only 2 points of failure are the fan, And the other not being as much a point of failure but lowering in its ability to transfer heat over time, That being the thermal paste between the cpu heat spreader and the metal block on the cooler. When you get an AIO there are a lot more points of failure and they are more likely to fail. When was the last time you ever saw a fan fail? Well with an AIO if something like the pump fails you probably won't even notice at first and it won't be until you start thermal throttling that you will know something is wrong. And unlike a custom loop, When an AIO pump fails you usually need to get a new unit and that can cost you if your warranty is out. Also the fluid going bad is a small possibility, But mainly if you are using one that has clear tubing and the company added coloring too it. If that happens then you would also need a new unit. Compared to most mid range air coolers the AIO does provide a slight decrease in temps but there are a lot of variables. The video below explains this in further detail.
If you want the good looks of an AIO go for it. Because in my opinion that is their only feature that is worth anything compared to air coolers. Custom liquid cooling is the best option overall since if a part fails you don't need to replace everything and you can add as much cooling potential as you want.