I can give part of the answer myself: There is a small pull down menue in the lower right corner of the device selector where I can select the "ES2" version instead of the "Production version". After doing so I can program my firmware into the board.
Remains the question how an "ES2 version" differs from the "Production version ". Any disadvantages ?
After PSoC3 chip was released, there were multiple revisions, with each revision having some fixes. The silicon revisions available are ES1, ES2,ES3/Production, where ES stands for Engineering Samples. ES2 silicon revision had many Silicon fixes. ES3/Production version silicon is ready for production and has most of the silicon fixes. At the time you purchased First Touch Kit, it was being shipped with ES2 Silicon.
CY8C3866AXI-40 is a specific Part Number. The part number convention is explained in the device datasheet Part Number Convention. In the string AXI, "AX" indicates that the package type is TQFP and " I " stands for Industrial.
As you have highlighted in your previous comment, the device selected in your device selector window should be the same as the device which you are trying to program.
I hope this helps.