So what confused me is that one IP address can work for the webServer but not for the webClient example. But the IP I identified above (using another machine) works for both examples.
Yeah, that's because I suggested the 169.254.x.y address specifically because it meant you didn't have to configure an IP address for your Mac if you used a direct connection between it and your Arduino.
Once you get past a direct connection it would no longer work in most cases--as you discovered. 
--Phil.