I've been tinkering with a variation on the theme -- something that can emboss paper / cardboard / thin sheet metal. 3D printed dies work great, but it's some rabbit hole! Lots and lots to learn.
Edit: it works if you put it through archive.ph: https://archive.ph/ruSeX
And here’s the model collection: https://makerworld.com/en/collections/453534-business-card-e...
Just pushing two blocks by hand and adding your weight will most likely be enough to make nice impression. The reason is that you have the inverted side - normally you would have just one plate pushing against some softer rubber so the paper has nowhere to go and you need a lot more force.
Tbh this roller design is needlesly complicated for business cards. Printing the rolls with overhangs will require supports. Roller press for graphics has some advantages like consistency of force and pressing of different sized/long pieces. None of which are useful here. Besides you wouldn't have emboss on the roll (unless you were printing infinite patterns) - you would press plate and paper through smooth roller press.
Here is a video of a desktop scale embosser used for just that purpose: https://youtu.be/5ZQHSsFnACs?si=DWwgTScwl5HXkwGP
The part where the embossing daisy wheel is shown is at 18:10.
Here are machines used at an industrial scale: https://www.maticagroup.com/technologies/embossers/
They are nevertheless called “embossers”.