LSL Guy should be along soon.
Happens all the time. Go watch DFW traffic.
May be some new rules but if the runways are XXXX feet apart, they can Land / Takeoff in parallel but as you saw, in close they often are staggered due to different speeds. Those speeds can be requested by approach control or the tower.
When I was mapping the the Trinity River through the metro-plex it took two trips just to set it all up, meetings, maps for them, I got my very own personal approach control operator when I was doing the flying. Lucky that I did it in one day as it was very difficult, scary, wild, fun & worked out great.
We had big airplanes ( we were in a little Cessna 310 ) going every which a way above us, below us, to the right of us, to the left of us as we flew into the corridor of death. I could hear controllers in the background calming big iron pilots that yes, they knew About the little plan they just missed bu a few yards ( really was not that close but they were very goosey about what they were seeing even with being told what they were in for by the center controls before they ever got near DFW. )
Several times it seemed like all I could see out the front was a whole lot of aluminium. Worked perfect, controller was most excellent, much fun and much sweat. Everyone danced well together.
Way back in the early 70’s I was using a Cessna 180 to work a strip camera doing pipeline recon for the DOT. That is one picture 70mm wide and up to 250 feet long. We only had one line that we got one take that long without having to break off for one thing or the other.
Had a line that I was running North bound on the West side of Love in field in Dallas one day. We flew these at 1950 ft with an RADAR altimeter in addition to other instruments and visual clues to hold the altitude as close as we could. That is not the deal, the deal was I had been working with one particular approach controller for over an hour & he knew what we were doing and what we needed. So as I was going up that side, I could see two airliners aide by side making their approach to the parallel N/W, S/E runways so I told him to tell me when he wanted me to break off & that I had them in sight. He told me to go to tower frequency as he had been briefed. (my altitude would also be their altitude on their approach crossing that N/S line I was flying. )
The tower said to just hold on, he though it was going to work out just fine. He got the two airliner pilots to get a visual on me, ( a 727 & maybe a 707 or DC-8 ) and to just make a normal approach. That it looked like I would cross in front of the 4 engine and behind the 727. As we all got closer together he said it looked like it was going to work well.
It did. I slid right across in front of the 4 engine and behind the 727 and it’s wake turbulence had sank just enough to not even ripple us.
When conditions are IFR, different separation rules / distances apply.
Many large airports have dual runways now, even more than twoand they are designed for the most part for simultaneous use.