That's pretty bad. Bad enough that I would suspect that it has not been assembled properly or has some serious manufacturing fault.
Having said that, the three Intertaps I have here are not without a fault. I have one that has started seeping a tiny bit in exactly the same location only after emptying three kegs through it. A second one seeps even more after two kegs, but it's not a running leak. Whenever I change kegs, I disassemble the tap, soak all parts in sodium percarbonate solution for about 10 minutes, rinse, lubricate with Lubrifilm Plus, spray with Keg King sanitiser and reassemble. I also use the tap auto-close springs and adjust the tension on the tap head such that resistance is just enough to make the self-closing work. That has resulted in seeping beer at the top of the tap. Nowhere near as bad as your leak, but bad enough to cause a build-up of sticky residue and a tap that is hard to operate - that is a problem, because the selling point of the Intertap is that it should stop sticky taps. It certainly fails to deliver on that promise in the setup I have.
I'll take the advice from mofox1 on board and will see if the self-closing springs are the source of the problem. It could be that them being too weak results in insufficient pressure on the valve shaft, which in turn causes seepage.
I might also give Keg King a ring to see if they have any ideas. On the one occasion I had to contact them previously, they were very helpful.