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Pravit
LOL

Tambakis
I came across the list with deminitive names, you can look up Игорь in it. There are some names I never heard :o
http://slovari.gramota.ru/portal_sl.html?petr_imsm.htm

I have no more ideas apart from Игорь/Игорёк.

Then it has no connection to his name.

Maybe his nick is Тигр?

Besides Игорёк it could be Игорян, Игоряша, Игорьман.
But all of them sound not very good except Игорёк.