Not the same. Games with parkour make movement look good even if a games journalist is playing. Games with platforming respect the player's right to fail and learn from failure to eventually make movement look good.
Elite: Dangerous - Menus
Rocket League - Parkour
Project Zomboid - Menus
Stardew Valley - Menus
Getting Over It - Parkour
This War of Mine - Menus
Outer Wilds - Parkour
Stacklands - Menus
Imagine a first person shooter with no menus. You just start up the game, and you're suddenly in a death match with some other random people. There is no customization for the type of death match. The setting and the weapon selection are randomly generated for you. At the end, you are shown a victory/defeat screen with no buttons. After 10 seconds, you join another match.
There is no pause button, no adjustment for mouse sensitivity, and no configuration for the screen resolution or graphics quality.
No menus. Definitely not a menu game.
The game also has no jump button, no stairs, and basically no Y axis at all. Definitely not a parkour game.
I've played Doom, Doom 2, and Doom 64. Their engines lack room-over-room architecture, but they do have a Y axis, and some parkour where you run from platform to platform (without jumping). They all have a menu.
Rather than playing the game, I spend way more time looking at how lit the build is going to be in POB, and then even more wasting all my currency crafting gear to try and make it work.
Menus all the way... unless you're doing Pillars of Arun, of course.
(The original calvin and hobbes comic is about the dad explaining how a point on the outside edge of a record travels farther, but still completes the same number of rotations as an inner point)