How to speed up playback speed like YouTube using Camtasia?
You don't do this in Camtasia as it doesn't appear that Camtasia supports pitch shifting at this point although there has definitely been some discussion of the topic for quite some time. 

There are alternate solutions however, ffmpeg has this capability through the atempo and aserate audio filters, I understand that you can do this with audacity and sox as well. If you have any interest in any of these approaches and would like further detail drop me a comment and I'll do my best to accommodate you.

According to @Mulvya you can also accomplish this with an ffmpeg build compiled to support librubberband You can compile it your self or there are Windows XP compatible builds available here which I've confirmed run under Wine

There's also a stand alone utility that I haven't used that you can obtain from the librubberband link above. It appears that that is limited to adjusting WAV files.

Some sources:

https://superuser.com/questions/292833/how-to-change-audio-frequency

https://superuser.com/questions/1118826/change-tone-pitch-for-file-audio

https://www.ffmpeg.org/documentation.html

https://feedback.techsmith.com/techsmith/topics/speeding_up_the_video_speed_without_effecting_audio_pitch