I believe that the Stern Entrance option is for tour companies needing tickets for groups of various sizes so no, that isn't what you wanted. From the coopculture website:
"This entrance (Stern) is accessible only for groups/schools or individuals leaded by an accredited guide....It will be necessary to show at the ticket office a list of the participants with their names and date of birth on headed notepaper. Without this list, the group will not be able to enter from this entrance and will be directed to the ordinary groups’ entrance."
It does look to me like you might be able to use your tickets for general access via the entrances everyone else has to use but I would contact them either by phone ( +39 06 399 67 700) or email ([email protected]). If you're OK with an informative guided tour of just the arena, coopculture has one that only costs 5 euros plus your entrance ticket.
https://www.coopculture.it/en/colosseo-e-shop.cfm
Look for this choice:
"Individual tickets with scheduled entrance time and guided tour" and choose the tour in English. If they've told you that it's OK to use what you purchased as your general-entry tickets, you would choose the free entrance + guided tour € 5,00 (a € 2,00 reservation fee will be added) option. Understand that this does not include the Underground or Belvedere but you'll largely get the same information.
You could also just rent an audioguide, or download Rick's audio tour for free, if bringing your own devices.
https://www.ricksteves.com/watch-read-listen/audio/audio-tours/italy
I'd just tag on to one of the group guides once you're inside
Sorry but freeloading guided tours annoys both the people who paid for the privilege and the guides who were not paid for their service. Finding oneself within earshot of one for a few minutes sometimes can't be helped but I wouldn't intentionally tag along with one.