Nothing like freshening old historical wounds to confront a new enemy. Of course the real purpose is to make the Turkish leader think thice regarding his meddling in Syria. Since Russia has also shown a willingness to send troops and to involve the Chinese as well, it is not mere bluster either.
Constantinople remains unfinished business with Eastern Christianity. Ongoing Turkish suppression of Christianity keeps it current. The conflict did not end then as the Turks have maintained a culture of supremacy over non Islamic peoples that remains largely ongoing and has mostly destroyed a huge christian population through coercion.
They who are dead cannot vote. Ask the Armenians. They were Christians and the first Christians to make it a state religion long before Constantine. Obviously their extermination by the Turks has never been explained as such. To do so would have fueled a massive war on the Turks during the twentieth Century.
Turkey is keenly aware that they are hopelessly vulnerable to a United Europe marching south and has been playing nice during most of the twentieth Century. Putin has just reminded them of just this.