Simplified ECC non-point public key example, how it works I know that ECC public key is in fact point on curve calculated by $(x,y) = k \times G$ , while $k$ is random and $G$ is the base point, it performs "Point addition" which involves some math behind.

However, in many ECC examples, take this as example:

domain parameters $(p, q, g)$ and private/public key pair $(b, g^b \bmod p)$

The generation of the public key is simplified to power of base point $g^b$, yet it works perfectly well for the example. Im puzzled by how a $(x,y)$ 2-dimensional public key can be reduced to 1-dimensional and still work?
However, in many ECC examples, take this as example:


That reference doesn't talk about ECC as all; instead, it talks about traditional El Gamal in the group $\mathbb{Z}_p^*$.