The circle is exactly the edge of the function domain. I suppose that the numeric algorithms of ContourPlot work mainly on sign variations, which do not happen across the circle. We must force some symbolic processing:
Region@ImplicitRegion[
Reduce[(x - 2) Sqrt[x^2 + y^2 - 5] == 0, {x, y}, Reals],
{{x, -3, 3}, {y, -3, 3}}]
