I often encourage clients to apply to Sloan because it requires a small up-front investment, if you have done the CV correctly. Also, the deadline is towards the end of the cycle so it's a way to leverage your efforts.
Cover Letter: They believe your past is the best indicator of your future - and so it indicates what you will bring to your class/ocean at Sloan. In the cover letter, try to get clear on your brand promise: what you deliver in every setting. And then provide a couple examples that illustrate this in STAR format.
The key is to succinctly articulate what the heck is so special about you, and for you to substantiate that.
Video: This is the first time they are asking "why Sloan" in the video which requires you to interview some past and current students, but the upshot of that your interviewees are writing your essay for you, if you ask good questions!
They are asking for you to include a bit about your experience. This surprises me, because they usually like to learn about a different dimension to you in this video. However I am sure they want to see how you might present your background in an interview. Make sure to communicate this experience in simple, relatable, universal language.
One minute is not a lot of time, maybe about 130 words. But do squeeze in a bit that helps them get to know you as a person, where you are from, maybe a bit about family (or not) but definitely your hobbies. You want to come across as energetic, interesting and well-rounded (not a boring robotic engineer.) Someone who you would enjoy speaking to at a cocktail party. That is the threshold.