You are correct in observing that the notes are not played simultaneously but very close. And no you don't have to be very fast, you just have to place your fingers above the notes as if you were about to play them simultaneously and then roll your fingers from left to right on the keyboard.
EDIT: Future readers - you must watch the video to see what the question is about. The screen shot may show different notes.
Use right hand fingers 1 (thumb) 2 - 3 and 5. Place them on the keys lightly touching them. Then roll your fingers starting with the thumb in a manner similar to doing a drum roll on a table top with your fingers. Continue holding each key down as you play each successive key. You are playing a D major chord but playing it with the roll instead of playing all four notes at once. Hold the chord after you complete the roll until it's time to play the next right hand note.
You will need to use the sustain pedal to sustain the chord until the next right hand note is played. From the linked vid I see that the next note (D4 - lower octave D note) is played while sustaining the D major chord (probably with sustain pedal) until you play this next lower D which I would play with my right thumb (the video indicates right hand for the D4 following the rolled D Major chord).
It takes a bit of practice to develop the coordination to get this technique right (fluid). But once you learn to do it, it comes naturally. Practice rolling in both directions. In the beginning you might find it easier to do this roll in one direction or the other. But you should learn to do it in both directions if you want to develop your playing skills. You can practice this on a table top or desk when you are not at your instrument.