A [general linear model](https://en.wikipedia.org/wiki/General_linear_model) doesn't generalize the function of $X$. 

Indeed assuming you mean $E(Y|X)$ where you have $Y$ (and independent errors) your suggestion would still be called a linear model (the conditional mean a linear function of the parameters).


Instead, a general linear model generalizes the covariance structure of the error term -- it includes the possibility of correlated errors.