I bought this watch "origo guide pro" off the Internet in used condition, however the backlight does not work. Could this be a blown bulb?

It can be several things to cause this, from the looks I would immediately say that the batteries needs to be replaced, it takes power to turn on the light and when it tried the power is taken from other components like the lcd, and never actually light because there is not enough power,
next it could be the bulb, it could be dead, short circuited. The issue is they are usually hard to replace and or irreplaceable, it needs the be rated the same for voltage a multimeter would help you a lot, to see if voltages are coming from the wires that connect to the bulb.
next the watch could be malfunctioning and may no longer have proper working circuity to run the backlight, this will be extremely hard to repair it will be better to replace the inside or take to a jeweler to have it repaired, in any event if you choose to repair it then you look for damaged parts and replace them- in the event that fails take you digital multimeter and trace the circuit to see if you can find the faulty part this requires you to have adequate knowledge of electronics and it would surely help to have the schematics to the watch--Good Luck.