Can power transformers be used with higher voltages?
It seems that the device was intended to run on two nominal voltages. It can be clearly seen that primary transformer has two taps: connecting terminals 11 and 12. I suggest you to remove the bridge between 13 and 12 and make a new connection to 13-11. 

Then you connect to the mains and measure the AC voltage between 14 and 12. If it's nearly 100VAC, then you're done.

You can do also in opposite way. Disconnect the electronics part, connect the mains supply as is from schematics with a bridge 13-12, 14-15. You would get a step-up voltage between 14-11. If the tap at position 12 is designed for 100VAC and tap 11 for 120VAC, now when tap 11 is supplied with 120VAC you should get  144VAC on tap 12. That would be a proof that connecting 120VAC on tap 12 makes no difference for secondary voltage.

As user Charles said, if the transformer is designed for 100VAC/50Hz and you connect to 120VAC/60Hz, the flux denisty is still nominal. But the secondary voltages are going to increase for 20%.