The big news in January was that Caesars will be the NFL's first official casino partner. The NBA, MLB, and NHL have all struck deals with various casinos, but the NFL has started with Caesars. The deal gives Caesars the ability to market the NFL with Caesars properties but doesn't include gambling or data feeds that have made deals with other leagues so valuable.
It also didn't hurt that the market rose sharply on hope the Federal Reserve will keep interest rates low for longer than previously expected. Caesars and other gaming stocks are dependent on a strong economy for growth, so easy money is good news for them right now.
News directly related to Caesars Entertainment wasn't particularly strong in January, but the market's bullish streak helped to push the stock higher. Gaming stocks are typically more volatile than the rest of the market, so when stocks rise as they did in January, investors are likely to see gaming stocks beat the market. I wouldn't read too much into January's move or the partnership with the NFL, though; at the end of the day, it's soon-to-be-released fourth-quarter earnings that investors will want to keep a close eye on.