I think you're missing the point: Yes, multiple pieces of equipment in the process adds some ms in between input, computer processing it, and screen outputting it.

The issue here is how much will ping time add to that when streaming a game. Consoles hover in the 100ms are depending on game. PC's it's highly dependent on video hardware, but I good gaming system, display, and keyboard/mouse will be around 70ms.

The issue of streaming game ping ms in part comes down to human reaction time, which averages around 200ms-250ms. Given this, you want a ping time that doesn't add enough latency to the setup to put you above that 200-250ms reaction time, or you start to perceive more noticeable input lag. Given 70-100ms baseline, you want a bandwidth ping absolutely no more than about 100ms on top of that.

The math squares with my personal experience as well. I've played a few streaming services, and when my ping gets to the 100ms area I start to notice a little difference. It's often sill playable, but if it gets higher it can be very distracting.