I could not find out the screen resolution, which suggests that the resolution is somewhat less than an ordinary non-hi-def TV. Such resolution is commonly between 720x480 to 360(across)x480 (elongated pixels) depending on the TV set vintage and quality.
I would guess the Eyeclops resolution to be something like 320x240 or maybe 480(across)x360
When the picture is projected at the 70 inch or so maximum size as advertised, the shortcomings of the low resolution will be much more noticeable.
I believe there is a good chance your kid may get tired of it quickly, especially if he notices that a regular TV gives a much better picture including when playing video games.
Meanwhile it appears that the Eyeclops is at least safe for children to use without adult supervision. Just about any "gbetter" projector will have a projection light that can damage eyesight if shone into someone eyes.