The resistor isn't necessarily a pull-up. Just that it is part of the pull-up "circuit". Circuit is in quotes because it's so simple it's hard to think of it as a circuit.
With the input floating (no pull-up or pull-down) there's no way to be sure what voltage is on the ECU input. With a pull-up, we're ensured that it's 5V if the switch is open. When the switch closes, it goes to 0V. This is also called a low-side switch since it switches GND.
In a pull down scenario, the resistor would be between the ECU input and gnd. Then the switch would switch 5v. This is also called a high side switch since it switches a positive voltage.
For what it's worth, some of the analog inputs have internal pull-ups in the ECU. Not all sensors are compatible with pull-ups though, so we leave a couple without pull-ups. Whether it has a pull-up or not (internally) is specified on the RescueKit.pdf (Dave linked to a template of it) sheet that should come with your ECU.
BTW, Lugnuts should be providing you with this kind of stuff, but we're happy to help.
Jason