This is how the video should should look like. I have the original video on the left.
What i did was load the original video on after effects, switch to alpha channel and export the video in Alpha channel. Then I created a new composition imported the previous export and the original video and placed them side by side for export.
Is this the correct way to do it ? because after the export the video on the right side lost it's transperancy.
Is there any alternatives that I could load the video as two layers and add some effect that could get the me the same output ?
It's not quite clear what you actually need and what for. An Alpha channel is just that - a greyscale representation of the transparency values, not actual transparency. In your case one would simply use the info on the right side as a matte to produce transparency. If you need something else, then simply render RGB+Alpha. I really think you have a wrong understanding of this stuff and need to figure out first what you actualyl need for the desired use case.