Confusion regarding the Definition of 2 Way Finite State Automata?
Unlike ordinary finite automata, a 2DFA needs only a single accept state and a single reject state.


Finite automata do not need more accepting states. Well, non-deterministic FA don't; just add two final states and appropriate $\varepsilon$-transitions. Deterministic FA, though, need multiple final states; above construction doesn't work, and Myhill-Nerode tells us that we indeed get multiple final states for some languages.


  Unlike ordinary finite automata, a 2DFA needs only a single accept state and a single reject state.


If you add rejecting states to finite automata (an easy enough exercise), neither do finite automata. Consider, for instance,

$\qquad L_0 = \{ w \mid w_1 = 0 \} \cap L$ 

for any regular $L$. Then, a finite automaton for $L_0$ can reject immediately if the first symbol is not a $0$.

In summary, I think the authors try to read meaning into arbitrary syntactical differences.

That said, note how 2DFA need a rejection state for the stated reason: there is no natural "end of computation".