Had a look at form.txt and mail.txt
The checkbox CF7 tags you have used in your form look fine. Also looked at the HTML generated via Firefox and this looks completely normal.
Your mail tags also look fine.
I am using similar CF7 checkboxes on numerous sites without any problems. All don't have Javascript deactivated though.
I tested your form and see that you do in fact have Javascript activated.
You may need to deactivate Contact Form 7 and completely delete it. Then re-install it into your WordPress instance.