I confirm. It's not an Arduino IDE specific problem because if you try to load that URL in your browser: http://arduino.esp8266.com/stable/package_esp8266com_index.json you'll see the problem is actually that arduino.esp8266.com is down. This has been reported here: https://github.com/esp8266/Arduino/issues/3035 and here: http://www.esp8266.com/viewtopic.php?f=26&t=14082
The issue with the boards disappearing is definitely a bug with the Arduino IDE. You can get the boards back by:
Add the URL:
to File > Preferences > Additional Boards Manager URLs Tools > Board > Boards Manager Wait for downloads to complete. Click "Close" (don't install the ESP8266 boards, you already have them installed) The ESP8266 boards will now appear in your Tools > Board menu again.
Note that the above Boards Manger URL can not be used to install the package because it relies on files at arduino.esp8266.com but if it was previously installed it will allow you to get the boards back.