In this video https://youtu.be/61jiIfW1sbI?si=gOJFchKVe_VpRZH6 an interesting principle is used. At least I find it interesting.
But the underlying principle isn't explained. The only thing the performer states is that he doesn't understand it himself. I'm sure some predecessors can be found in The Jinx, or other old manuscripts. Or is it a Martin Gardner thing? I don't know. But I want to know. It feels like it's related to the forcing matrix.

So if there is anyone out there who knows the origins (prefered) or can explain the principle, I'd be realy grateful. And I will probably make an online tool to create new numbers.

I don't know the original source for this version, but your instincts are correct: it's a forcing matrix with an extra column (each card represents a column), so a 5x6 matrix. Removing one card removes a column (one of the six), leaving a standard 5x5 forcing matrix.

As removing one of the columns also removes the seed for that column the forced total must be equal to the original seed total (222 in this case, for the 5x6 matrix) less the removed seed. Any one of the six columns can be removed, so there are six possible forced totals.

Of course it's that simple! Thanks!
I would still like to know who originated this idea and explore other applications of this idea.

Here's an improved set of numbers for the BINGO Prediction:

#1 - 14 27 43 60 74

#2 - 11 24 40 57 71

#3 - 12 25 41 58 72

#4 - 7 20 36 53 67

#5 - 10 23 39 56 70

#6 - 3 16 32 49 63

There are two improvements. Most importantly, the numbers under each letter are those that actually correspond to that letter in BINGO. Secondly, you can use a simple (no subtractions) formula to calculate the predicted total (so no crib is required). To do so, start with the # of the unused card. If it is odd, add it to 190; if it is even, double it, then add it to 190. This yields the desired value.

Of course, you can still prepare a crib if this is easier for you. The crib would be: #1 = 191; #2 = 194; #3 = 193; #4 = 198; #5 = 195; #6 = 202.

The root of the good old forcing matrix can be found here:
Walter Gibson: Date Sense, in: The Jinx, no 41, Feb. 1938, p. 279 (using a calendar)
The first source explicitly using the matrix seems to be:
Maurice Kraitchik: Mathematical Recreations, W.W. Norton & Company, New York, 1942, p. 184