Not a stupid question. Yes, the part of the card you indicated with 6 contacts needs to physically touch the reader. Here is some info on the ISO standard for contact “smart cards”. Here is some info on contactless smart cards.
The other reason it’s near impossible to convert those types of cards is that the chip that sits under those metal contacts is typically a “dual channel” chip, meaning it can handle both contact (the metal pins) and contactless in the same chip. That means to convert it, I would have to somehow physically remove that chip from under those metal contacts and then connect a new antenna to it… but that chip is under a glob of epoxy resin and removing it basically destroys it… I don’t have the patience or equipment to do it.