Answer
No, the statement is not violated.
Work Step by Step
$\vec{E_1}$ and $\vec{E_2}$ are the electric fields generated by 2 different charges. However, when we draw the electric field line at point P, or at any other point, we need to consider the vector sum of all the fields there.
There is a single electric field line passing through point P, pointing up the page, and it does not cross any other electric field line.
This situation is correctly shown in Figure 21.28c.
