I haven't even watched the video, but I can tell you that it's a trope about how you basically craft a character for the intent of hooking up with another character and nothing else and that their relationship is forged on rather shallow things. You can even go much more shallow and have one character be almost a literal cardboard cut out that is only there for relationship fodder and doesn't actually contribute anything.
The only thing they are right about in this regard is that Ashi was made to be Jack's lover. It's obvious given what Genndy said was his inspiration for Samurai Jack, dreamed of exploring alien worlds with his crush. The rest of the trope doesn't fit at all though. Ashi is too independent, she has A sense of wonder, but not a childlike one, she acts like an adult and treats situations well enough and also knows the difference between right and wrong and her own mistakes.
The cusp of the trope, is that the "born sexy yesterday" should in reality, been taken advantage of and that is their argument. Jack is a 70 year old world weary veteran and Ashi is maybe 20, still fresh to the ways of the world and in their eyes "needs someone to look after her". Jack entering a relationship with her is taking advantage of her.
It's a load of bullshit.