A video with $30$ minutes length, played at $33.33\%$ faster speed that equates to $22.5$ minutes. Where are the extra $2.508$ minutes?
Yes the math is $$\frac{30}{1.3333} = 22.50,$$ but my intuition is that the result should be $20$ minutes. How do we reconcile that "$2.5$" minutes extra?
You have two problems. I think you are trying to say that if it is played $\frac 13$ faster you expect it to be done in $20$ minutes. First, $\frac 13$ faster is $33.3\overline 3\%$ faster, not $30\%$ faster. That would make the running time $\dfrac {30}{\frac43}=22.5$ minutes. The second is that if you want to reduce the running time from $30$ to $20$ minutes, you need to go $50\%$ faster. As you are reducing the time by a factor $\frac 23$ you need to increase the speed by a factor $\frac 32$