Definitely sounds like valve lash to me, good video, it helps a lot.

 

It doesn't have push rods, but I think you are thinking lifters. It does have lifters, but they are called hydraulic lash adjusters and are essentially lifters. As far as connecting rods, most internal combustion engines have them, except for Wankle Rotaries.

 

Pull your serpentine belt off and if the noise goes away look into the A/C compressor. Don't run it long with the belt off because your water pump will not be circulating coolant

 

Update.

Car sounds worse now. Ticking sound is gone completely and now anything above 2000 rpm sounds like ice cubes being crushed. A really painful grinding noise is how I would describe it.