My phone with 3000 mA/h battery is 7.8 mm thick, 70 x 138mm size and has the same Snapdragon 810 CPU. Weight is 130g, volume 75.35 cm3, volumetric mass density 1.73g/cm3, water has 1g/cm3. As all I need is that total volumetric mass density is less than water has, I can add a styrofoam or hollow space in it (it must let in no water inside as it will increase density otherwise). So, as a weight remains the same (consider styrofoam has no significant weight), I need to increase the volume/thickness 1.73 times, so 7.8x1.73 = 13.5 mm, add say 1.5 mm to be safe, an here you go, 15 mm for this particular hardware. If the phone used more plastic and less metal, it could be a bit lighter, so I guess something like 12-13 mm is quiet possible. But yeah, price is too low to be possible, unless they take off the shelf phone and just add a styrofoam case to it. If the off the shelf phone used is the same price as my xiaomi mi4c ($250 for 32 GB when I bought in december, $217 now), then it is theoretically possible.