Also occurs to me that it's odd they actually caught it on camera at all. There's a lot of sky out there and fighter jets are fast, not to mention they can employ beyond visual range weapons also.
In this video the jet flies straight into field of view and launches a very short range missile at it. At that kind of range it would be easier/cheaper to use cannons I'm sure.
First, modern military aircraft can move pretty slowly when required, as well as very quickly. At airshows many can hold formation with a prop-driver aircraft, and if you look at the video, the Mig has a high angle of attack which indicates slow speed. The camera's looking down, and we're looking straight down the Mig's nose when it fires. As someone else mentioned, it's also unlikely the aircraft approached unnoticed. The Georgians and Russians aren't good friends these days, and their border airspace will be heavily monitored.
Second, that UAV clearly has a good zoom lens (why else would it be up there?

which adds foreshortening effects to the footage.
The missile's in flight for what, 3-4 seconds? The R-73 (seems like a safe bet) flies at up to Mach 2.5, but even if it only averaged about Mach 1 on that flight (allowing for acceleration, climb, manoeuvring, and relatively low level use) that puts the aircraft at well over 1km away... unless my maths is even worse than I suspect.
I see nothing dodgy about that footage at all. I just wish all similar military aircraft encounters ended that way, with no loss of life. Then I wouldn't have to feel uncomfortable about being so impressed by them and their capabilities.
Anyway, UAVs are spy-planes whichever side of the border they're flying on at the time. That makes them fair game if you ask me.
Andrew McP