There're two ways to embed a YouTube video into a path. 

First method is to do it via Assets. 

Go to Assets > Create Asset. Under asset type choose "Video content":

As the next step choose YouTube and insert the link: 

Finalize the steps. Now, under assets sorting by creation date it's possible to see the newly added content:

Second method is embedding YouTube video via external content. 

Go to Manage Paths > Content > Add step > External content:

On the YouTube video click to the "Share" or "Teilen" button below the video. Share modal window will show up. Click on "Embed" or "Einbetten":

Copy the video link exact way as it's shown here (no quotation marks): 

Paste the video URL into SmarterPath, hit Save and finish the step: 

Now the video should be available in the Path.