Most TV's nowadays have a game mode that can kill lag. A lot of the Panasonics actually have low if not nonexistent input lag. That Said I do use a monitor for my offline setup and it was much faster than my old TV(32in Vizio).
I used some Samsung 2ms G2G , that had nearly 15ms of Input lag that broke , but b4 that i did bulk of my Pro E-sports FPS PC gaming on CRT Viewsonic Professional grade monitor which had 0 input lag , perfect response and 120 refresh , walk into any BestBuy you won't finding anything that flawless but for games these days I'm way to casual and play on a 120hz 60Inch gimmick of a TV from LG , when i have my PS4/PS3/Wii U powered up . Soon to pick up BenQ's XL2720G ( drops sometime early 2015) to return to my PC Roots .
That is what I meant when I said delay. I should have said "input lag." The disparity between when your console/computer knows something (inputs) and when it is actually showing that information to you. You bring up a very good point, though. This is why most people don't focus on the input lag since it isn't put out into the forefront in regards to marketing. That is because most people don't play games that require very precise timing. Let's be honest, a 0.07s discrepancy in input is not even worth mentioning to most consumers.
also the delay you're seeing in the video is another misconception on response time & refresh rate which have minimal importance in the bigger picture ... this delay is "mostly" based on input lag and no gaming flat panel'd VA / IPS / TFT / or consumer high branded LEDS/LCDs/Plasama manufactures display the input lag details on their products , super nerdy review sites like tomshardware / blurbusters / displaylag tend to have charts that you need to pick the best monitor for your needs