Myriounis started his playing career with Kronos BCE.
In 1991, he was selected along with Fragiskos Alvertis and Nikos Oikonomou, to join the Greek Basket League club Panathinaikos.
In 1993, Myriounis was a starter with Panathinaikos (his teammates were great players such as Nikos Galis, Arijan Komazec, Stojko Vranković, and Tiit Sokk), and with them, he won the Greek Cup title.
During the next season after that, he played for Apollon Patras, and he was a Greek Cup finalist with them.
Myriounis also played with the senior Greek national basketball team at the EuroBasket 1997.