I'm not sure if this is saying the observed growth at the time wasn't exponential (at all), or just that the doubling time was 'nowhere near' 7 days. Either way not sure I agree.
Here's the chart reproduced (using the data as it stood at the time, Oct 4):
And here with an exponential curve fitted (the orange dashed line) to the data:
The fact that an exponential curve is a good fit is much easier to see if we use a log scale (on which exponential curves are straight lines). These are exactly the same lines as before, just with different vertical scaling. Clear the data is following an exponential trajectory:
Now doubling time: just over 11 days according to this fit. Perhaps you can argue this is 'nowhere near' 7 days, but it still results in case numbers reaching 50k by end of Oct; at most a couple of weeks later than in Vallance's warning.
Updating to today's data: doubling time just under 10 days