What you are referring to is the same weakness in regard to malleability that is also applicable to (non-hashed schoolbook) RSA. In Elgamal an attacker can (in practice) not decrypt the transferred and encrypted message, but he can modify (factor) it and is able to determine the effect of his modification.
Let $y$ be the original encrypted message of the plain text $x$.
In the course of action the encrypting party would transfer a data tuple to the destination party, namely the encrypted data $y$ and the ephemeral key $K_E$, which is public, but only valid for this one message (since Elgamal is probabilistic).
An attacker could simply replace $y$ by the product $n \cdot y = y_{NEW}$, where $n$ is any factor at the discretion of the attacker.
Let's call the altered encrypted message $y_{NEW}$ to make clear it is different from the original encrypted data $y$.
The receiving party would then decrypt the result as $n \cdot x$, with $x$ being the original unencrypted data from the sender. Of course the receiving party does not see the the two factors but only the product and is left believing (or not) that the data is integer.
Why does this work?
When receiving the tuple the decrypting party would first compute the needed multiplication key $K_{M_{DECRYPT}}$ from the public ephemeral key $K_E$, the secret exponent $d$ and the prime $p$, and of that find the inverse $K_{M_{DECRYPT}}^{-1} \mod p$, or at least have a notion of the inverse for calculation purposes.
Decryption then works by multiplying the received encrypted data $y_{NEW}$ by $K_{M_{DECRYPT}}^{-1}$ modulo $p$.
Let's call the decrypted message $x_{RECEIVER}$ to make clear that it is the result of the decryption on the receiver side, and that it may not necessarily match the original message $x$.
$x_{RECEIVER} \equiv y_{NEW} \cdot K_{M_{DECRYPT}}^{-1} \equiv n \cdot y \cdot K_{M_{DECRYPT}}^{-1} \mod p$
and since $y \equiv x \cdot K_{M_{ENCRYPT}} \mod p$ (see encryption)
$x_{RECEIVER} \equiv n \cdot y \cdot K_{M_{DECRYPT}}^{-1} \equiv n \cdot (x \cdot K_{M_{ENCRYPT}}) \cdot K_{M_{DECRYPT}}^{-1} \equiv n \cdot x \mod p$
The substitution of $K_{M_{ENCRYPT}} \cdot K_{M_{DECRYPT}}^{-1} \equiv 1 \mod p$ works since both keys are equivalent, even though they are calculated separately. This can be demonstrated as follows:
$K_{M_{ENCRYPT}} \equiv K_{PUB}^i \equiv K_E^d \equiv K_{M_{DECRYPT}} \mod p$
since
$K_{PUB}^i \equiv (\alpha^d)^i \equiv \alpha^{di} \mod p$
and
$K_E^d \equiv (\alpha^i)^d \equiv \alpha^{di} \mod p$
for the secret exponent (private key) $d$ and the probabilistic exponent $i$ and a primitive element $\alpha \in \mathbb{Z}_p^*$.
The result of the decryption ($x_{RECEIVER}$) is thus the original data $x$ multiplied by the factor $n$ chosen by the attacker.
This is why (schoolbook) Elgamal is called malleable.
As previous authors have mentioned, other more advanced variants of Elgamal are used in practice, in particular variants resistant to this demonstrated weakness.
