I feel bad bumping this old thread, but I am sadly facing the same problems. I am trying to do the Morroblivion mod. I followed the steps and only included the 3 files. Whenever I launch the game using Oblivion.exe it gives me the OBSE not detected error. When I click new game, it gives me the beginning video of Morrowind but the gameplay is of Oblivion.
However, when I click obse_loader.exe, it launches the game without the detection error. But the beginning video is of Oblivion and the gameplay is that of Morrowind. It's very weird.

Hello. Sorry I am 5 years late. Though I have a quesion for this. Do I need to overwrite the data folder or not? If I was not supposed to be, that is all I need to restart again.

No, the data folder and the src folder are only needed if you want to make mods using script extender.

If you did install all the files from obse_0021.zip and allowed it to overwrite the files in the data folder, it doesn't actually overwrite anything, because the data folder doesn't have any files with those names. (unless you have installed OBSE before)

If you installed the full package from obse_0021.zip, and not just the 2 files as I suggested, then you need to overwrite
obse_loader.exe in the games root directory, with the GOG version from obse_loader.zip.