Look at how Bowser raises his cup and nods in agreement.

Look how he looks at his THIGHS first

I think the animators checked with Nintendo about how Bowser would canonically drink coffee.

Actually, Nintendo checked with the animators.

http://www.nintendolife.com/news/2013/04/nintendo_told_disney_how_bowser_should_hold_his_teacup_during_wreck_it_ralph_production