Your mouse probably needs a USB host to initialise it before it turns on its LED. Try it on a powerbank or USB charger, and I'll bet the LED doesn't light!
I'd bet there is no data connection to the 'bad' connector, as I doubt they've included a two port hub chip, and you haven't seen a new hub enumerate. Odds are it is power only and will power a USB powered 'tchotchke' that doesn't need too much power just fine.
Of course its non-compliant as the 'good' connector will be wired straight through, so it cant negotiate for the extra power drawn by whatever you plug into the 'bad' connector, so even if not faulty, its defective by design!