Any "lead" Intel might enjoy over AMD currently, is clearly offset by the fact that for less money you can get the same performance (Or close enough to it that it won't matter in real world usage, because, let's face it, if you need 144fps and you can get it from AMD for 250 bucks, what sense does it make to pay 350 for Intel just to get 156fps that offer you no real benefit? ) or for the same price get a product that offers much better OVERALL performance, especially, as you say, if you plan to do more than JUST game, and are streaming, recording, running other applications, browsers with many tabs, or whatever else it is you are doing while gaming. Or, for games, and there are a lot more of them these days, that see significant improvement from more cores and threads, or applications that do as well. And every cycle more games and more applications get optimized for taking advantage of those additional cores and hyperthreads so it makes more and more sense to look at options that give you that.
That puts you in the conversation with AMD for most people. And for anybody that wants to save some money on their build, that probably puts you in the same conversation. I'm not against either camp, I just don't see anything from Intel lately that is making me inclined to stick with them even though I've done so for the last several systems I've built myself.