Hm is it louder when cold? It actualy sounds like a leaking exhuast manifold/cracked manifold???
Or, like you say tappets, usualy more of a knocking noise on this engine layout but depends. One might not be pumping up, If you have flushed the oil, and it is a lifter, i would say it almost certainly needs replacing. But, if you can put up with the noise, it wont do much harm.
Either way i would expect it to be louder when cold! Other causes could be the big end? Hate to even mention that but rule that out first, they can start as a light clicky rattle!
my 1.4L engine has a similar problem to this! but is more of a knock than a click now, I thought it was the lifter but i think its the small end bearing now. I wouldnt expect that to go on a GTI engine tho!