That first video only calculates the cals from carbs, not how many cals you should be on the cut.
I would normally say to just use an online calculator but if you're studying this stuff and making nutritional plans for clients then you should really get it down.
However if you want to cheat, MyFitnessPal does all the work for you and is easy to use as a logging tool throughout the day.
The ratio of protein/carbs/fats can vary, you don't have to stick to what he's saying in the video. If you want lower carbs and higher fat then you can tweak the ratios to suit your preferences, body type, tolerance to carbs/fat etc.
I prefer to work out a percentage but say 25/55/20 for P/C/F.
If your maintenance cals are 2200 then the calorie ratio will be 550/1210/440.
Then we can use "x4 for protein or carbs and x9 for fat" and it will give 137/302/48 which is the grams of each.
If you want to cut, then take 200-400 off the maintenance cals and do the maths again. Opposite if you want to gain weight.
You will need to go over it regularly because as your weight changes, your maintenance cals will also change. This is the same if you're trying to put on or lose weight.
As Jiggers said above, for it to be effective, you really need to dial in your maintenance cals though. Log what you're eating and get as close and consistent to that 2200 or whatever you think maintenance is and record your weight over a week or two. If it goes up or down then your number is wrong.