Decided to Google my dad's coin today. I assumed when I found it that it wasn't a game token! Very similar to OP (tho, not in as good a condition), 'cept, I assume, struck in a different city[?] (Mine says "Eon," or possibly "Kon.")
Your coin would have been minted in Constantinople where his would have been minted in Nicomedia. @DanL If you want to learn more, look at wildwinds.com under Byzantine, Emperor Justin II and use control F to search for Follis. You should find a match there.
@DanL, the second (obverse) photo of yours is upside down. (The "M" is on the reverse and the two figures on the obverse.) The obverse shows Justin II and his wife Sophia seated side-by-side. The mint is CON = Constantinople and the year is G/II = 6+2 = 8. His dates are 565-578 and year 8 = 572/3. The reference is Sear, Byzantine Coins and Their Values, #360, which happens to illustrate the same year, but with officina Gamma instead of Epsilon.