What the Economist article seem to fail to mention: "In the accelerator-on-a-chip experiments, electrons are first accelerated to near light-speed in a conventional accelerator . Then they are focused into a tiny, half-micron-high channel within a glass chip just half a millimeter long." From: Stanford's own article: http://news.stanford.edu/news/2013/september/slac-chip-accel...
Take into account, though, that accelerating electrons into near light speeds is not too difficult anyway. They are thousands of times lighter than protons, for instance, which is what the LHC works with most of the time.
Actually the reverse is true. Protons emit less synchrotron radiation, making it easier to make accelerators in a ring shape. Electrons eventually radiate as much energy as it takes to accelerate them, creating a barrier.