There are no CPUs designed to "stream and game at the same time". They are simply designed for heavy multi-tasking, of any kind. Of course, that falls under that category so in some sense it's true but they are certainly not "designed" for streaming while gaming. It just happens that streaming while gaming is a heavy multi-tasking environment.
It will do just fine. I'd be sure not to skimp on the amount of memory (RAM) though, multitasking hits memory usage pretty hard if you have enough things running, or processes that are rather demanding.