Ok... since this is a technical subject... we need to be a bit more picky about the details that are being discussed... You have to consider ALL of the components to determine what speed limitations may or may not exist.
bigone started by asking if Cat6 would handle the required data... The problem with the question was it was only about the potential speed of just the cable and didn't take into account the port limitations that Tony brought up... and what was not mentioned, the total speed the switch is capable of handling, which myself I can only mention it since I don't know it's full specs because that is outside the scope of my knowledge as well.
So to address cabling specs first.... see the chart I've attached that lists the specs for Cat3 up to Cat7 cabling. It shows for Cat6 as mentioned, 10Gbps @ 250Mhz frequency and I believe this is for a 100 meter run of cable. Longer runs will degrade that performance but probably not enough to worry about here even if it is worth knowing about it.
Next you need to know the speeds the ports on the switch are capable of handling. 1 Gbps is pretty good for most needs as Tony mentioned.
What wasn't mentioned is the total processing the switch can handle. Most switches, except the most expensive ones, can't handle all of their ports operating at their rated speed. They can only process up to a certain percentage of that total. Now Tony did mention that the NVR was only connected to a single 1 Gbps port so that is where it will be "bottlenecked" at. But we still need to know there is also a processing limit among all of the ports. In this case the limit will be the port the NVR is capable of handling... but if traffic wasn't limited to just that direction ( to/from the NVR ) then you would need to consider all of the traffic and their routes in the rest of the network.
As I type this... I don't know we established what speed port the NVR actually has on it. That also needs to be considered as another possible bottleneck if it were to say have just a 10/100 Mbps port on it.
To sum it up... it isn't just about the pipe being used but the complete network of them and the limits that each bring.