I read through the link provided on this little automotive power supply, and it's got the neat feature that it:
is an intelligent automotive ATX power supply for in-car applications with maximum 180 Watts output, designed to provide power and to control the ON/OFF switch of an ATX motherboard based on ignition status.
X5-ATX will send power off signal to motherboard 30 seconds after the ignition off, and will cut off the +5VSB rail after a further pre-defined amount of time (90 or 600 seconds depends on user setting), to prevent the battery from being run out. X5-ATX constantly monitors the battery voltage, and when battery level drops below 11.2V from more than one minute, X5-ATX will shut down and re-activate only when the input voltage is larger than 9V.
A nice feature for controlling a computer, or other device that has a similar momentary power switch. It even comes with a 2 "pin" wire to connect the MB power pins to itself. A regular power switch is just a temporary shorting of the 2 pins. Apparently, this will momentarily short the 2 pins itself whenever it thinks the "ignition is on" (whatever that means, power on the ACC connector is on?). So this PSU becomes the power switch, and "presses it" itself. When a motherboard has it's power swtich pressed (shorted) it should connect/short the sense and ground connectors, which should fully turn on the PSU.
You also say "I expected it to simply short the 2 pins (emulate a button), but it doesn't happen" but it should be happening. Is your Ignition (ACC) wire getting power properly? Or, maybe the DELAY jumper is delaying power on (it's vague in the description of just how it powers on) maybe 30, 90 or 600 seconds? Or, maybe it's just broken.
"But" you say "I have a different device to power up, not a motherboard" so you really don't care how a motherboard power switch works, do you. All that matters is how your "different device" powers up, and that's a different question. If it's got a momentary power switch, just connect the little PSU power wire to the device's switch, and let the PSU turn on the device.
Or, if there's no momentary switch on your mystery device, and if the power supply doesn't turn itself on automatically, then just jumper the sense and ground connectors (like Journeyman Geek mentions) and that should at least turn "on" the PSU.