But the Changelings need love to fuel their energy which King Sombra has none, like Princess Celestia said his heart is as black as night and having the power of shadows, traps (not talking about stairs), dark magic, fear and curses, I think he can easily defeat Chrysalis and her Changelings and you should not pay attention to the lack of screen time he had and pay attention to what he actually did, and I'm not talking about the stairs, that was just a part of his old castle that Twilight found, he actually did almost take over the Crystal Empire in a short amount of time (near the middle to end of the 2nd episode) than how long Chrysalis took to almost take over Canterlot (the entire 2nd episode)
The only people who think Chrysalis would win this one are people who don't like Sombra. There is absolutely no reason he wouldn't win this. Assuming he can turn to shadow like in the episode, Chrysalis' army would not be able to land a single hit. And considering Shining Armor's performance against Sombra, all he would need is engulfing Queen Chrysalis once, ONCE, and he could lock all her powers completely. Then Sombra would drown the whole area in darkness and tear the Changelings apart with his crystals.
Sombra has black magic, smoke and crystalline powers that can not only make him intangible but also increases his range of attack and defense. Plus, if we're assuming Chrysalis and her army arrived in the Crystal Empire during Sombra's rule, there's absolutely no love for them to feed on, which means Chrysalis won't be powered up like she was with Celestia. Sombra can brush aside the non-magic using soldiers, and then content with Chrysalis one-on-one when he uses his crystals to, oh I dunno, entrap him and the queen in a closed off space. Chrysalis is fucked because she isn't powered up, and from what we can tell, she's weaker than Celestia without love to power her up.