How so?

The important parts to include on a sketch are that the function is monotonically increasing, has an asymptote at x=1 [0], intercepts the x-axis at x=e (approx 2.7) and quickly becomes almost flat. Both graphs agree on these points.

Wolfram Alpha is using the complex logarithm (https://en.wikipedia.org/wiki/Complex_logarithm) to extend to x < 1; Google isn't. I'm fairly sure an interviewer would expect a sketch that looks like Google's, perhaps with a comment that achieving ln(ln(x)) < 1 is possible (only) if the ln function is allowed to take complex values.

[0]: For values of x < 1, ln(x) < 0, so ln(ln(x)) is not a real number.

You're right, the plot is correct. I didn't look closely and thought the vertical asymptote was at x=0, but actually it is at x=1 as you mentioned.