The mini gun in the live action video fires about 80 to 100 rounds of 7.62x51 (also known as a 308) per second. The cheapest I was able to find 308 rounds online was $679 per 1k (can get a little cheaper if you purchase steel cased rounds). He fired for about a minute straight so about 6k rounds or $3800 of ammo not counting the links to put them together or the labor to link them. So maybe I was wrong in my first assessment but still $4k to shoot for a little over a minute? He has a better job than I do. I am a bit jealous though.
This assumes I IDed the gun correctly, however it looks to me like an M134.