What You need to look for is a
Vending Machine Dolly. It's similar to an "Appliance Dolly" but generally beefier. I used to use these to move Coin Op Soda machines which can weight up to 1000lbs without any problem.
The one you linked to is decent, with the back legs down they look like this:
So the two key features here are the built in strap that you can use to wrap around the machine and tie it to the dolly (so it doesn't tip off). and the smaller support wheels on the back, those lock into place allowing you to just tip the machine back and pull it along without having to support the weight while you use it.
Also notice that the handles are really tall you can get these at different heights, you want one that's about as tall as the machine you're moving so that the back is fully supported and you can grab the top of the handle from above the machine (this is key if you're moving up or down stairs). Also notice the plastic rails covering the metal so that the dolly doesn't scratch up your cab.
the oval tread looking things on the bottom are there to help you slide up and over stairs.
I bought mine used for $50, so definitely check around. it took me a few months of looking before one popped up, so depending in your time table you may not have that option.
Of course there are also super fancy ones that automatically climb stairs or act like a fork lift to load into trucks.. but these usually cost a few grand.