oximeter CMS50 to arduino uno?

Hi,
I would be interested to interface a Contec oximeter CMS50E to an arduino uno R3.
manual: http://www.pulseoxstore.com/CMS-50E.pdf

it uses an USB cable that connects to a PC.
the serial settings and bytes to receive/send are demonstrated here

Though I'd like to connect that oximeter USB cable direct to the arduino uno
I have a USB A female to B male adapter, so I can connect the oximeter to the arduino uno USB:
oximeter <-> USB cable <-> adapter <-> arduino uno through USB

I set Serial.begin(19200) and programmed the arduino to write to EEPROM any Serial.read values, but Serial.available and Serial.read are not getting anything both when I switch to "live" mode and "upload stored data" mode.

Is connecting through the arduino USB actually going to work?
Or do I need to connect the oximeter USB cable to analog pins for serial com? How would I go about it?

Your device is a USB device as is the Arduino but both are slave devices. This means that they can only communicate to a host (usually a PC) but they cannot communicate with each other. There are shields that incorporate a USB host interface chip but be prepared to implement the "USB driver" yourself for unusual devices.