How I see it is
skills are one thing.
Internal power and aiki are another.
Traditionally, "aiki" is going to only be an application/usage of "ki" power (which has a number of terms applied to it by different arts); "aiki" wouldn't be a separate subject where it would be called, for instance, "the aiki power".
"Jin" is the force itself, although it can be correctly called "qi", since it is considered to be the physical manifestation of qi. Tohei and others in Aikido traditionally refer to the power itself as "ki" or more limitedly as "kokyu" or other similar variant-names (like "rei-ki") of the ki-skills. "Aiki" is usually reserved in usage to the way Inaba Sensei described it. But if you look at "internal power" and "ki" they are traditionally inseparable... the one supports the other, although it's possible to have the general ki without having the specific jin/kokyu-type skills, as Tohei demonstrated by pushing over the zen monks.
Traditionally, though, "ki" and all it's facets are considered one general subject. Most of the skills and throws in the 3 videos discussed so far, Nishikido, Kuroda, and Kono could generally be called "aiki", but still the usages are simply variations of "ki power" or "kokyu power"; if the hands are used to do the application then technically the power could be called "elbow power" for easily apparent reasons.