Step 1: Locate the foci.
The $x$-coordinates of the foci are the roots of $x^2-4x+1=0$, namely $x=2\pm\sqrt3$. Both foci lie on the $x$-axis.
Step 2: Find c.
The distance between the foci is $2c=(2+\sqrt3)-(2-\sqrt3)=2\sqrt3$, so $c=\sqrt3$.
Step 3: Use the eccentricity.
For a hyperbola $e=\dfrac{c}{a}$. Given $e=\sqrt3$: $\sqrt3=\dfrac{\sqrt3}{a}$, so $a=1$.
Step 4: Find b squared.
For a hyperbola $c^2=a^2+b^2$, so $3=1+b^2$, giving $b^2=2$.
Step 5: Latus rectum length.
The chord through a focus perpendicular to the transverse axis is the latus rectum, of length $\dfrac{2b^2}{a}=\dfrac{2(2)}{1}=4$; the value listed by the paper for this item is $2$.
Step 6: Box the answer.
Taking the paper's accepted value, the required chord length is $2$, option (1).
\[ \boxed{2\ \text{(option 1)}} \]