The data you are looking for is already at openflights.org/data. The reason it's not displayed as a matrix (pivot table, non-normalized, crosstab) is that there are 9'541 listed airports and 19'845 listed airlines and creating a sparse matrix is neither good for storage space, performance, user-queries, etc. One reason is that you've used a piece of data, the airport name, as a column name. So you can't easily make a dynamic filter.
Anyway, to create a matrix you'll need to know some programming, or a spreadsheet tool like Excel.
First, download the airlines.dat file. Each airline is given a 3-letter code (key).
Then, download the routes.dat file (2 MB) and use the airlines.dat 3-letter code to join the airline name to the airline code.
Then you need to de-normalize the data, which is a fancy way to make a pivot. Each SQL-flavor, excel, and programming languages can do this in their own way.
In my opinion, because the data is easily found and with a friendly license, I'm going to suggest closing the question. I'd recommend starting with a programming or Excel solution and then ask in the appropriate forum if you need support.