What is the equivalent resistance in this part of the circuit?
Current does flow around the resistor. Note that the resistor is completely shorted out (its ends are connected together with wires, meaning the potential difference across it is, by definition, zero).

Another way of looking at it is that the resistor is in parallel with a wire/short-circuit (i.e. \$R_{wire} = 0\$). You can calculate the total resistance of any resistor in parallel with a short circuit by using the basic simplified formula for parallel equivalent resistance of two resistances:

$$
R_{eq} = \frac{R_1R_2}{R_1 + R_2}\\
$$

With the values in your problem...
$$
R_{eq} = \frac{(100)(0)}{100 + 0} = \frac{0}{100} = 0
$$