Horgan has been going on about stuff like this for years. He wrote a book in 1997 called "The End of Science" which I read and thought was completely ridiculous. My recollection (possibly faulty as it's been quite a few years) is that he came across as very anti-science and wandered off into religion later in that book. It feels to me as though he WANTS science to fail at some point.
I don't know why he seems hell-bent on convincing everyone that we're going to run out of things to discover, but I just don't buy it.
Even if we manage to get to the "bottom" of Physics some day that's cool and all but it's hardly the end of much. The biology of even simple cells is fantastically complex and there's lifetimes worth of discovery left there. Also even if some day we we know most or all of the "rules", the possible applications of these simple rules are virtually infinite, so no scientists or technologists or explorers are likely to be unemployed any time soon.
Every time humanity thinks it knows everything, someone thinks up a clever new idea for measuring things and boom, a whole new world of complexity opens up. There might be an end to the turtles at some point, but I'm not worried