The question has been answered. For clarity: "Yams" are a specific potato that is shaped roughly similar to a human leg (feminine). The slang was used predominantly in the 1940s to 1960s to describe an attractive woman's legs. "Gams" means the same thing. (Ref: Watch any "Hogan's Heroes" WWII re-run, or Audie Murphy /Colombo detective 1960s era TV show where the men use slang refer to women's legs as "yams" or "gams" - you may not like it, but case is closed.
The play comes in affixing a feminine description of Mitt Romney's legs as "yams" is to say he's not all quite man and more girly in his disposition and his legs are more womanly shaped vs. a muscular man's leg. it's an innocuous swipe, since the slang if directed towards women's physical attributes and is not used in America for males--ever. So, if it is...
You basically have two things to read into this - 1) Mitt Romney is being called out as kind of effeminate, either in his appearance or some kind of trait. So much so that his legs are actually more attractive if he was a female than having the legs he has as a male. This might not actually be true at all, but the author of the article is using this slang for a purpose. It's an attack on his character or how he's facing or doing his job in politics is more womanish vs. being tough & manly--read the full article and you'll see the author's points. ..but the author isn't only calling out Mitt Romney, he's calling out all politicians as feminine -- and here's why:
The main article (I counted five) is from Vanity Fair (2015), then passed around/edited by other syndicated columnists - all refer to a scheduled boxing match Mitt Romney, a politician was to have with World Heavyweight Champion, Evander Holifield. Many politicians have played sports; even "Bird legs" Romney but, he attended more sit in's opposing the Vietnam War in the 1960s vs. playing any sports. Being a sports champion is not a pre-requisite for success in politics - even women can be a politician or hold political office. Therefore, the swipe taken at Mitt Romney is innocuous in that a politician is going to bare his "chicken legs" in a boxing ring dressed in boxer shorts, and since he's going up against the World Heavyweight Champion, the only thing the author eludes Romney brings to the fight worth seeing will be his "yams."