It should be compatible. It has a serial mode. You can test if the VFD is working but using the test pin, it's active low signified by the line over it. Just power the VFD with +5 and short pin 16 to ground. It should display all characters as a test. This is on page 7.
All the signal voltages are +5 or 0 so it's good. You will need a larger +5v supply it's very specific that you need +5V at a max of 1A so you may want a 1.2Amp (min) supply for it. You can get a +12V 3A wall wart and use a linear regulator.
I'm not sure if this is compatible with
but it sure looks like it. There is a very interesting RXD line that's supposed to be the serial input which I'd like to try.
I repair devices at work that use these but have not yet tried them with an arduino. I will be doing so soon as they are too nice a display not to.
I'd just wire it up as the instructions on the tutorial state. Page 8, table 10 has the pinout. Pins are not the same as an LCD but I think the chip acts like the one on an LCD. It should do no harm if not as the voltages are compatible.
This may be the controller IC
It could be a 16311, 12, 15, etc not sure