The men broke into the machine at Fun Central in Westover Road on the morning of August 31.
They took a box which contained tickets and receipts, causing more than £500 worth of damage to the machine before fleeing.
CCTV images have been released of two men officers would like to identify.
Police community support investigator Amelia Vaughan said: “We have been carrying out enquiries into this attempted burglary and we are now in a position to issue images of the men we would like to identify as part of our investigation.
“I would urge anyone who recognises them to please contact us.”
Anyone with information is asked to contact Dorset Police at www.dorset.police.uk or by calling 101, quoting occurrence number 55240134468.
Alternatively, independent charity Crimestoppers can be contacted anonymously online at Crimestoppers-uk.org or by calling Freephone 0800 555 111.