If I use a splitter, I need an HDMI cable to the grabber (connected to the Pi) and another one to the TV. That should be the logic...
But I've seen a video with a splitter only connected to the grabber. From there, a USB cable to the Pi and an HDMI cable to the TV.
I can't see how it's working, but if this is the way, the stick device is not appropriate.
Is it?