How disable internet download manager's video download option from my youtube videos?

you are using youtube API so the question is that you can't do anything as they'll continue using HTTP protocol which is stateless and thus can be downloaded !

A workaround you can do is to make browser detection script in javascript which will detect presence of IDM Plugin ... Once you detect the presence of IDM then you can disable the video embedding and not enable it till the user manually disables the IDM Plugin