Before going to play in the United States, Glyniadakis played as a youth with Kydonas of Chania, Crete, Greece. He then started his professional career with the Greek team Panathinaikos. After playing at Panathinaikos, he moved on to Peristeri and then to AEK Athens.
In May 2007, he signed with the Italian League's Virtus Bologna. In September 2007, he returned to AEK Athens. However, he was waived on October 1, 2007. He then joined the Greek League team Maroussi. He was the MVP of the last 16 week 1 in the EuroCup 2008–09 season.
In July 2009, he moved to the Greek EuroLeague team Olympiacos Piraeus. With Olympiacos, he won the EuroLeague and Greek League championships in 2012. After a season of playing for Astana, he signed with Lietuvos rytas of Lithuania.
On 31 January 2014, Glyniadakis signed a contract with Cypriot side APOEL, and helped his team to win the Cypriot League championship at the end of the season. On October 30, 2014 he was signed by Turkish team Royal Halı Gaziantep. On December 23, 2014, he moved to Romania and signed with Enegria Rovinari for the rest of the season.
On August 14, 2015, Glyniadakis signed with Les Lions de Geneve of the Swiss Championnat LNA. In November 2015, he left the Lions and signed with the Greek club Nea Kifissia for the rest of the 2015–16 season.
On July 21, 2016, Glyniadakis signed with the Greek club PAOK.
On August 4, 2017, Glyniadakis signed with Kymis.
Glyniadakis was selected by the Detroit Pistons with the 58th pick in the 2003 NBA Draft. In the 2005–06 season, he played with the Roanoke Dazzle of the NBA D-League. He played with the Atlanta Hawks during the 2006 NBA preseason, but he was cut before the regular season began. He also played with the Albuquerque Thunderbirds of the NBA D-League, and with them, he won the D-League championship in the year 2006.
Glyniadakis was signed by the Seattle SuperSonics on November 5, 2006, and appeared in 13 games with them, averaging 1.3 points per game, before he was waived on January 4, 2007. He played for the Boston Celtics in the 2007 NBA Summer League, in Las Vegas, Nevada.
Glyniadakis was a member of the Greek junior national teams. With Greece's junior national teams he played at the 1997 FIBA Europe Under-16 Championship, and he won the bronze medal at the 1998 FIBA Europe Under-18 Championship. He also played at the 1999 FIBA Under-19 World Championship, and at the 2000 FIBA Europe Under-20 Championship.
Glyniadakis was also selected to the senior men's Greek national basketball team for the 2008 Summer Olympic Games. He won the bronze medal with Greece at the EuroBasket 2009, and he also played at the 2014 FIBA World Cup.
Note: The EuroLeague is not the only competition in which the player participated for the team during the season. He also played in domestic competition, and regional competition if applicable.5x Greek League Champion: 1998, 1999, 2000, 2001, 2012
2x EuroLeague Champion: 2000, 2012
D-League Champion: 2006
2x Greek League All-Star: 2004, 2009
2x Greek Cup Winner: 2010, 2011
Kazakh League Champion: 2013
Kazakh Cup Winner: 2013
Cypriot League Champion: 2014
1998 FIBA Europe Under-18 Championship: Bronze
EuroBasket 2009: Bronze