My issue is not about card type (yet) as it seems that ESXi does not support my smart card reader.
I had to disable native USB driver to make ESXi see USB devices at all.
# esxcli system module set -m=vmkusb -e=FALSE
After this USB reader was detected by VMkernel but pcscd does not claim my reader, USB device remains available for pass through.
2017-05-14T10:29:37.746Z cpu2:65945)<6>usb 2-2: new full speed USB device number 7 using xhci_hcd
2017-05-14T10:29:37.895Z cpu2:65945)<6>usb 2-2: New USB device found, idVendor=08e6, idProduct=3437
2017-05-14T10:29:37.895Z cpu2:65945)<6>usb 2-2: New USB device strings: Mfr=1, Product=2, SerialNumber=3
2017-05-14T10:29:37.895Z cpu2:65945)<6>usb 2-2: Product: USB SmartCard Reader
2017-05-14T10:29:37.895Z cpu2:65945)<6>usb 2-2: Manufacturer: Gemalto
2017-05-14T10:29:37.895Z cpu2:65945)<6>usb 2-2: SerialNumber: 67EF18E2
2017-05-14T10:29:37.896Z cpu2:65945)<6>usb 2-2: usbfs: registered usb0207
2017-05-14T10:29:38.900Z cpu1:67166)<6>usb 2-2: device is available for passthrough
Running pcscd on foreground with "pcscd -f -d -a" does not result any log messages when reader or card is connected. Card reader product id 3437 is listed in /lib/pcsc/drivers/ifd-ccid.bundle/Contents/Info.plist. However pcscd seems to be very old, 1.8.5 which is from 2012, so it might have some issues.
I also tested this on CentOS Linux 7.3 which has pcscd 1.8.8 and on that pcscd recognizes my reader and card.