He played for the Dinamo Sukhumi in the late 1960s and later continued his career in Stavropol, Minsk and Kislovodsk before joining CSKA (Tbilisi).

Gabeskiria helped to create Sukhumi-based Tskhumi soccer club (which played in the newly formed Georgian football league) where he served as a president.

When the city of Sukhumi fell to the Abkhaz separatists on 27 September 1993, Gabeskiria along with other authorities from the Government of Abkhazian Autonomous Republic (Zhiuli Shartava, Raul Eshba, Mamia Alasania, and others) refused to leave the besieged city and was captured by Abkhaz militants and North Caucasian mercenaries.

Based on video materials, Human rights documents and witness accounts[1] of the event, G. Gabeskiria, Z. Shartava, R. Eshba and other members of the government were dragged outside of the parliament building and forced to kneel by the Abkhaz/North Caucasian militants.

[citation needed] On 27 September 2017, Gabeskiria was posthumously awarded by President Giorgi Margvelashvili the title and Order of National Hero.