Yes, that's a standard 622 aka "700C" rim that can fit any 700C tire. However, you'll want to also pay attention to the width of the tire.
From the way they say "622-13 700C*20*19MM" it should mean that the rim bead seat width is 13mm, but the extra "20*19mm" stuff makes things seem a little unclear to me.
It's likely that it's 13mm wide and the "20*19MM" is intended to be the tire width they expect you to mount on it.
However, 20 and 19mm width 700c tires are somewhat rare. 23mm and 25mm are much more common and are sizes that should work well on a 13mm width rim.
According to Sheldon Brown, if the rim is 13mm wide, you'll want a 18-25mm wide tire. If it's 19mm wide, you'll want a 28-44mm wide tire. If you're not sure, 25-28mm is a safe in-between range that should fit either width ok and will still fit within the brake and other clearances of bikes with narrow clearances (typical road, track, racing, "go fast" bikes).
Measuring the bead seat width accurately is hard without the right tools, but if you hold up a ruler or measuring tape to the rim and measure the inside width, it should be easy to tell 13mm (1/2 inch) from 19mm (3/4 inch).