Long comment
It is not a typo.
Having said that, the Theorem is a sort of "preliminary" result, that will be superseded later by the Soundness and Completeness Th for FOL (Sect.2.5, page 131-on).
The key fact (stated in previous Enderton's comment) is that:
If $\Gamma$ tautologically implies $\varphi$, then it follows that $\Gamma$ also logically implies $\varphi$. But the converse fails.
Thus, with insight, having that
for FOL $\vdash \text { iff } \vDash$ holds,
and having shown that $\vDash$ and $\vDash_{\text { TAUT}}$ are not equivalent, we can conclude that also $\vdash$ and $\vDash_{\text { TAUT}}$ are not equivalent.
IMO the $(\Rightarrow)$ part of the theorem is not very interesting: the proof technique (by induction) is basically the same used for Soundness.
The interesting part is the $(\Leftarrow)$ part: the fact that considering the set $\Delta$ of logical axioms as "additional assumption" is enough to have derivability is proved in a quite simple way (about 10 lines), compared to the complex proof needed for Completeness (5 full pages).
A second interesting feature of the Theorem (IMO) is that it shows the benefit of Enderton's proof system, compared to "traditional" FOL proof systems, like that of Mendelson, using two rules of inference: $\text { Modus Ponens }$ and $\text { Gen }$ (this approach to FOL is due to Frege (1879) and Whitehead & Russell's Pricipia Mathematica (1910)).
Enderton's proof system uses more quantifier axioms, and in this way it can avoid $\text { Gen }$ rule: this fact has the big benefit of simplifying the Deduction Theorem.
In this context, the Th can be read as showing that the additional quantifier axioms are enough to replace the misssing $\text { Gen }$ rule.