You are able to preview embedded touchpoints somewhere else in 2 ways:
In touchpoint
You can enter the preview link in the touchpoint:
When clicking 'Live Preview', you will go to the entered URL in preview mode.
Note: This does not work as a targeting URL. You can use the current URL rule in the targeting option in the settings menu.
Paste touchpoint={{touchpointid}} to trigger preview mode
You can also trigger the preview mode manually. Copy your touchpointID (the last series of numbers in the touchpoint editor) and paste it onto your website. For example:
Note: if the touchpoint does not appear, there might be an error in the configuration, although you correctly preview the touchpoint.