I'm not sure what you mean by "the same method as Blooming Panic", but if you're using a Windows machine you need to:
1) download the correct zip file (the one labelled "-pc")
2) unzip the file by right-clicking on the file and choosing "extract all" or "extract here"
3) go into the newly-made folder and find the application file, which should be called "Obscura" and launch that. If you have an older Windows machine then you may need to launch "Obscura-32" instead.
The process should be similar if you're a Mac user. Extract the folder from the zip file, then go into the folder to launch the executable. If the launch file isn't working, you may need to see if your anti-virus program hasn't blocked or deleted the game files; OBSCURA isn't a risk to your computer but some anti-virus programs don't like playing unknown games.