The only real "gimmick" from this century that has stuck around was motion controls, and even then in much more limited fashion than in Gen 7. A few Switch games use motion controls, and some games do support gyro controls on PS4 & PS5, but that's about it. Other gimmicks like dual screens have essentially died off.
All the big innovations that have stood the test of time and become industry standards were from the 20th century, and Nintendo either created or popularized most of them. The D-pad, the diamond-shaped arrangement of face buttons, shoulder buttons, and rumble all made their first appearances on Nintendo controllers. They were also the first to include an analog stick on their controller, as they had the foresight to realize how important that was for 3D games. Too many Gen 5 games suffered from bad controls because they were designing 3D games to work with Gen 4 controller layouts (that's why tank controls were a thing, and why they should have stopped being a thing on the PS2,).
Sega had their 3D Pad released a month after the N64 debuted, launching it alongside Nights into Dreams, whereas Sony's Dual Analog wasn't released until 1997. Sega was the one to introduce analog triggers with the 3D pad, and that became the norm the following generation. Sony's implementation of two analog sticks became the norm as it was better to have a right stick for looking/moving the camera to complement the left stick being how you move around, so that was the one of two things Sony did that became standard, the other being the two pairs of shoulder inputs as opposed to the single pair found on the PS1 gamepad's progenitor, the SNES gamepad.
Actually, now that I think of it, motion controls were around in the 20th century as well. Mattel had the Power Glove for the NES. Sega had the Activator. Broderbund had the U-Force. None of them were very good, though. Motion controls that were actually good didn't exist until Gen 7, and while Nintendo and Sony introduced their motion controllers (Wiimote and Sixaxis) at essentially the same time, Nintendo made far more prominent use of it.
Overall, I'd say game controllers owe the most to Nintendo. There's a clear family/evolutionary tree going all the way back to the NES controller.