Because it is way more efficient (built on 14nm process while the 650 is on 28) and that makes a significant difference in battery life which is the phone’s strongest point. On other hand most users wouldn’t be able to feel the difference in power in most tasks. While Xiaomi faced some backlash by the enthusiasts for using it, I think it was a good choice overall and it’s no surprise that it easily became their best selling phone and the best selling mid ranger in China and India where they sold it officially. They used 625 in a lot of their phones last year and are using it once again in the Note 4’s successor.
By the way, you’ve written 825 instead of 625 in the table.