My girls have the exact same Nishiki mountain bikes. The purple one is actually a year newer but has significantly worse tread wear. Any idea why?
Kid bike tyres tend to be on the cheaper-end of materials and wear quite fast. Most kids bikes end up where the rider out-grows the bike, so a long-life tyre is less important. I suspect the newer purple bike has slightly lower-grade rubber in the tyre than the older bike.
A child's bike would likely does less than a hundred miles in its entire life.
Riding on a low pressure can also accelerate wear on the tread.
Another cause for rear tyres to wear is when the rider is a little hoon and does M4D SK1DZ which wear flat spots. Do that enough and the tyre simply wears down in the middle.
However, I can still see tread blocks on both tyres - there's a complete carcass to wear through before that tyre needs replacing. Also, the more-worn tread will be smoother and more comfortable for the child to ride due to its lack of knobs. And it'll be faster/less effort required.
I see no need to replace that tyre, unless its getting a lot of punctures, or its cracking/crumbling.