This is a second system that you are primarily using for streaming from the other system? Then I'd say it's overkill. Streaming/recording by itself is not terribly difficult. A laptop can stream if you have the correct inputs. You might also consider a dedicated streaming card/device. Which should be more than capable and offer significant cost savings over buying a whole new system.
You might be able to find a second hand system like a refurbished dell office PC that would be capable of handling the stream for a pretty reasonable price. You might have to add a GPU to help with encoding but even then you could probably put something together for a few hundred dollars.