I am 100% certain that Travelify does support newly introduced playlist functionality. Here you can see it in action on my test website:
There is no such widgets in WordPress as of today, however it is possible to add playlists to sidebar as well. All you have to do is to enable shortcode functionality
do_shortcode in widget area. It is likely that some plugin have already done it for your but if playlist shortcode is not working, you can enable it my adding these lines of code inside
functions.php In best case scenario use Child Theme.
// Enable shortcodes in widgets
do_shortcode functionality won’t come in theme by default because it is so called plugin territory and therefore is not allowed to be added inside themes distributed via WordPress.org
If you still having problems with playlists, make sure to disable all plugins and see which one block it from functioning. Most likely it is some Soundcloud or similar plugin with exact same functionality. It can be due to server configuration as well but in this case many other functions such as oEmbed wouldn’t work either.