Speed is nothing without a good end product. To pile on the clichés; a good craftsman never blames his tools.
Yes, spending £4.00 instead of 50p on a roller sleeve is going to get you a better piece of equipment, but in the hands of someone rushing and doing things in the wrong order, they're both going to leave you with a ****ty job.
The guy in the video indisputably knows how to handle a roller, but he's working on a new build with no flooring or furniture to worry about, a fresh surface and arguably no Mrs. Soandso coming round to inspect the skirting etc.
I've seen you posting a lot on here asking about tools, materials and techniques, and in my opinion you can apply this to all your questions:
1. Buy from a decorator's merchant - ask for advice.
2. Have a plan. Take the time to stand in the room and work out the most efficient way to tackle it. Usually I prep, ceiling, woodwork and walls, but that's me and every room is different. A plan is your bible.
3. Preparation of surfaces is next to godliness, or something. Spend more time on prep and less time worrying. No prep = you can only polish a turd so much.
4. Be relaxed with a brush in your hand, eye up your line and pull the brush through it at a decent pace. Never drag paint out too far and never wet more than 2/3rds of your brush. If you do, stop and clean it out.
5. Same with a roller, don't keep rollering when there's no paint left, but avoid skidding on too much paint. Consistent eveness is the aim.
6. Patience, a steady hand and logical progression.
Hope that helps.