What's the calculation in the Tweet Count? Does it involve a secondary data source? If so that's your problem, you can't sort on a secondary data source.
Tableau doesn't have support for ascending/descending sort of measures, it sorts dimensions based on a measure. For measures there are the data source order or manual sort options as you saw. What Shawn was referring to is that you can't sort a dimension based on a measure from a secondary data source.
Since you're talking about wanting to sort the Tweet Count and it's being used to draw a line chart, there's a different way to go about this. You have the Tweet Count in the view as a discrete (blue) pill, if you change it to continuous then you will have an axis and can choose to have the axis sorted ascending or descending.
As for the dates, you have year, month, day, and hour in the view as discrete pills, which generate headers. If you want to have a continuous axis showing the hour, then you're going to want the date value (also called datetrunc) version of Hour, to get that click on the Hour pill and choose this:
That will turn it into a green pill with a continuous axis. You'll still have a lot of extra headers, though, with vertical lines breaking the mark line, to connect the lines you'll need to get rid of as many blue pills as you need.