I've known Laura for a while now; she is a long-time participant in the socionics community and has made other videos before. This video didn't change my opinion of her type; I think the same options present themselves, with the same apparent contradictions, as we will explore below.
Laura consistently presents an open, tolerant, and accommodating view of others, and dislikes conflict, rudeness and roughness, and unpleasant interactions. She believes everyone has inherent worth and tries to approaches others with tact when possible. My observations of Laura in the community match this: she has very little inclination towards conflict or abrasiveness, and prefers if people could just all get along.
All of this is a strong indicator of Si/Ne values.
Laura is also curious and focused more on the intellectual side of life: her jobs have consistently focused on information, she doesn't do a whole lot to beautify her environment, and would prefer not have to deal with physical maintenance if she could. She got a short haircut because it's easy to maintain - one tactic an intuitive might use to avoid dealing with sensory complexities. She is always thinks of the long-term future, and loves the feeling of mastering a new skill, as well as experiencing new cultures by traveling (potentially if not actually in her life).
This suggests that Laura is much more likely an Ne ego type than an Si ego type. Traveling and skill acquisition are common Ne themes. Laura does show some ability to maintain her life, and a tendency towards stability in her career and finances: she has worked in the same career for over a decade with little change, and although she mentions feeling stagnant, she also views the prospect of unknown change or risk (in the "starting a business" question) as "scary" and a threat to the status quo, therefore something she would not really do in practice. This points to relatively higher priority for + ability to deal with Si, and therefore more likely Si mobilizing than suggestive. This goes hand in hand with the lower Se and higher "activation energy" needed to kick oneself into gear and realize possibilities in one's life.
But we see more ambiguity in how the rational IM elements might fit into Laura's psyche.
For Fi: on the one hand she speaks very clearly and directly about what she seeks in relationships ("loving me, supporting me", trustworthiness, emotional support), and likes it when people cry or "show their vulnerability."
On the other hand, she also uses Fe in describing all of her relationships: doing "fun stuff together" (mother), "being fun to be around" (sister), "good sense of humor" (father).
This suggests that maybe Laura is one of the types with some ambiguity between Fe and Fi, namely IEE or LII.
But there are other clues. Laura also describes not having close, deep friendships, only lots of acquaintances. And although her work does involving interacting with people, this seems to drain her; she sees people as interruptions at her work and wants to find one where she's more "behind the scenes".
She also seems a bit insecure about relationships in general (maybe this is not so type-related, but in context it could be). She describes needing help in relationships, how to relate to others better, and was not very tactful as a young child, but learned how to be as she got older.
When it comes to logic, Laura is good at organizing information, and explains her role and the structure of her work very clearly, right off the bat.
Overall I think LII is the best fit for Laura. She is a natural organizer, is dependable and reliable in her work, and while she is in touch with her emotions, she isn't really a people person either. She is sensitive to criticism, yet has a strong sense of fairness and civic duty. Fairness, which as I see it, is one of the distinguishing themes of the LII.