Interesting. We are looking to reduce electrical usage 25% so that our usage matches the output of the solar array we installed. We already installed a tankless water heater to only heat water on demand, which is nice, but sending all that hot water down the drain is a waste. Since the tankless heater requires a certain flow rate to trigger the heating element, I don't know how it would work with a shower like this, but recirculating already hot water will require minimal additional heat to maintain the temp. It must have a supplemental heat source in addition to the pump.
The up-front cost is huge (spork's estimates seem conservative for a 1 shower/day family), but there is a recurring cost of filter pods as well, which you can probably only get from the manufacturer, and they will probably gouge you on the consumable. Many companies will sell a system nearly at cost and make all their money on consumables.
I wonder if this is patented or if prices will come down with competitors. It is a great idea, and I wonder how hard it would be to make a DIY version with a hidden recirc pump, heater and filter in the basement where the drain is. Something where the filter is universally available with lots of suppliers.
WIFI is probably to track how much water and electricity is saved vs. a standard shower. People who drop loads of cash on a green technology like to be constantly reminded of what a great thing they did and how wonderful they are for doing it. Our solar array production is tracked and we receive a monthly summary email update.