I do not have any experience actually reloading the bootloader, but did find this article that may be useful: Sparkfun - Installing an arduino bootloader. In this article the Arduino ISP ino is used to flash an Arduino with another Arduino. This sketch appears to come with a menu option to select the correct and official bootloader for your Arduino Uno.
Hope this helps.
p.s. I assume that the Uno close runs the exact same bootloader as an original Uno (which is very likely).
I thought the same thing. The board is marketed as a clone of the Uno so it should have the same bootloader as the Uno. Which may be true for some boards. But this board would not run if I flashed it with the Uno bootloader. It would only work if I used the mini bootloader.
Whether this is normal or due to a problem with the board I can't tell
Hmm, it could be that the clone is actually not a "Uno" - in the end these boards just have an Atmel microcontroller, and they can name it anything they want I suppose ... Does it work with the other bootloader? If yes, then I'd leave it that way 😉