The explanation seems adequate.
Another method to express "X is a subtype of Y" is by stating that "X is assignable to Y". Therefore, you could reword the definition as follows:
If A is a subtype of X or B is a subtype of X, then A & B is a subtype of X.
For instance, if you have a value of type Cat & Warm, it can be stored in a variable of type Cat, Warm, and even Animal due to the fact that Cat is a subtype of Animal. In essence, Cat & Warm is a subtype of Cat, Warm, and Animal.
In the given scenario, A {x:1} and B {y:1} are not assignable to X {x:1;y:1}, but I is assignable to X.
Indeed, A cannot be assigned to A & B, and similarly, B cannot be assigned to A & B. The clarification implies that A & B can be assigned to A and also to B.
When stated that "X is assignable to Y", it signifies that having a variable x of type X is permissible:
const y: Y = x
Hence, the following code segments are acceptable:
const a: A = a_and_b
const b: B = a_and_b
However, these expressions are invalid:
const ab: A & B = a
const ab: A & B = b
Example (playground link):
type A = {x: 1} | {z: 42}
type B = {x: 1}
type C = {y: 2}
function f(bc: B & C) {
const b: B = bc // Acceptable because B & C can be assigned to B
const c: C = bc // Acceptable because B & C can be assigned to C
const a: A = bc // Valid since B is assignable to A, thus B & C is assignable to A
}
function g(b: B) {
const bc: B & C = b // Not valid, does not work the other way around
}
In your specific case, when invoking the functions f with a and b, you're essentially replicating what's happening in the function g. This will generate an error because A cannot be assigned to A & B, and likewise, B cannot be assigned to A & B.