From the video, 1ms feels real time, but with 5ms you can still notice the lag. So wouldn't it be more appropriate to say "4ms is significant"?

That would require a real-time OS, I suppose.

“Realtime” doesn’t imply faster. In fact often the opposite. It just means certain timing constraints will be satisfied, often making explicit what the costs (tradeoffs) are.

Yes, the constraint here is 1ms.

You only need a real-time os if you're guaranteeing maximum latency.

Which is exactly what was asked for.