The Rakuten Mini in the video is 106.2 x 53.4 x 8.6 mm at 79 grams with a 3.6” screen, so much smaller and lighter than the iPhone 4. The Rakuten Hand (also in the video) is 138 x 63 x 9.5 mm at 129 grams with a 5.1” screen, a bit taller and thicker but also narrower and lighter than the iPhone mini.
Unfortunately, the hardware, software, and interoperability of those Rakuten phones is too limited and outdated.