No, the NKN software will not require high processing power and can be run on personal computers, smartphones, routers and switches. That is one of the design goals of NKN, and the reason we are putting serious research hours into Cellular Automata. Naturally the more processing power and link capacity a node has, the more reward it can generate from relaying traffic and help record transactions.
We might be able to run the software on even smaller embedded devices (e.g. IoT devices), as long as they run on Linux. Our initial software overlay should be able to run on any Linux system in user space. We do not intend to build the software in Linux kernel space in the very beginning. Even though that means greatest efficiency and potentially smallest footprint, it will complicate the deployment model and slow down initial adoption.
In the long run, we do intend to have deeper stack integration and optimization with network equipment vendors, down to hardware and even ASIC level. That will give us the quantum jump into next level of transmission capacity and user experience for the NKN network.