How and What do pullup resistors do?
The pullup resistor is the one at the very top of the circuit. Between Vcc and Y+. (As explained in your quoted paragraph!)
They use a "significantly higher resistance" in order to make the measurement more sensitive = more reliable. So that there is a very clear, unambiguous detection of a touch.
I believe by "total resistance of the touchscreen" they mean the "Y+ resistor" in series with the "X- resistor" since that is the total path to ground.
"High" means that point in the circuit is very nearly equal to Vcc.  And "Low" means that the point is much lower because the "Y+ resistor" in series with the "X- resistor" have pulled it down against the pull-up resistor.