That picture looks like it's actually the opposite, HDMI to RCA. When looking at ebay
listings it seems some of them have pictures of both RCA to HDMI and HDMI to RCA connectors for the same product.
Anyway, we have a Converter box with that generic case where I work, which is RCA to HDMI 720P/1080P. I don't have an example picture at hand, but produces the most awful looking image imaginable full of Y/C artifacts. The RCA inputs on the TVs give a way better picture.
I'm not claiming all analog -> HDMI converter boxes are bad, but with these generic OEM boxes it's hard to say what you get. I do some analog capture via HDMI myself, but that's via a DVD recorder and at standard 576i, and some others here have experimented with devices that output via SDI (professional HDMI analogue). For capturing it's generally better to capture at standard resolution and scale up later after processing. Scaling makes it hard to to any post-capture work, and the scaler in the device will be much more limited than what a computer with lots of processing power and time can manage.
If you have a need for live analog input to a TV or monitor that only has HDMI, I would rather consider a used DVR or an AV receiver with HDMI out. For game consoles there are also specialized devices like RetroTINK.