China did censor this year's inauguration, in a directive to media outlets. This's not surprising due to Trump's rhetoric towards China.
It is forbidden for websites to carry out live streaming or picture reports of the inauguration.
There isn't any definite article that states if China broadcasted that year's inauguration. However, I did find an article published by state media CCTV.
Obama's first inaugural speech was not planned to be censored initially, until he mentioned "communism".
In an article by The Washington Times, it states:
Chinese who stayed up into the early hours to watch the historic swearing-in ceremony, looked on as the state-run China Central Television (CCTV) abruptly cut away from its coverage of Mr. Obama’s address when he spoke of how “earlier generations faced down fascism and communism.”
The censors didn’t wait to hear the rest of the offending sentence — “not just with missiles and tanks, but with sturdy alliances and enduring convictions” and proceeded to mute the Chinese interpreter, abandon the shot of the U.S. Capitol and seek refuge with a flustered studio anchor.
In conclusion, it's unclear if the 2013 inauguration was censored. However, this year's is definitely not the first that is censored.