As I thought unless Asana has added an import option I haven’t heard of your only option is to create each project in Asana and copy/paste the tasks from the CSV file to the Asana project and repeat.
The file you want is task.csv
Open it in a spreadsheet.
Filter on completed not FALSE.
Move the project_name column to before the name column and sort on project_name and project_sort.
The name column is the tasks.
For each project copy the project name and create it in Asana.
Then copy all the tasks that match that project name and paste them into the Asana project.
Repeat for each project.
I hope that helps.