I'm not misreading anything. Your link is pretty clearly referring to the laws on treason;
https://www.law.cornell.edu/uscode/text/18/2381
Which, yes, includes similar "giving them aid or comfort in the Unites States or elsewhere" language.
Also, your source is from 1918. That literally predates the law text as it stands today, which was written in the 1940s.
The insurrection on January 6 was trying to overthrow the authority of the government and prevent the legal process of the election. It definitively fits under the definition of "insurrection or rebellion".