I'm curious if single threaded* games/applications that were CPU limited when the P4 originally came out run better on the 13900k with the same code.

That was my impression from games at the time, that they were coded with an expectation that clock speeds would keep going up in the future. But they didn't and the games probably run just as bad now as they did before.

And even in the Pentium 4 days, AMD CPUs managed similar performance as a Pentium 4 while running at lower clock speeds (which was a problem with some games that tried to auto-tune their performance-settings purely based on Pentium 4 clock speeds, even if you had an AMD CPU – thankfully at least in the Maxis/EA case, those settings were easily hackable, though, and could be easily adjusted to better match non-Pentium 4 CPUs, too).

Right. But not clock speed.