Given that Sony's famous futuristic racer WipEout features craft which float just above the track surface, it's reasonable to assume that Nintendo's F-Zero - which predates WipEout by almost five years and also contains anti-gravity racing - would have provided the main inspiration.
However, lead designer Nick Burcombe has revealed in an interview with Push Square that although a Nintendo game had a massive influence on WipEout's conception, it's not F-Zero.
Speaking about how the idea to fuse a techno soundtrack with high-speed racing occurred, Burcombe said:
I was playing the last race of the 150cc cup in Super Mario Kart on the Super Nintendo, and I’d muted the game audio so I could hear my own music. Age of Love was playing on the stereo in the background. I’d tried about ten times to beat the last race, and on this final attempt I was in second place by the time the music was about 2:10 mark. The final laps took place where the track was at 2:45 and it felt so exhilarating; it was as if the music was pushing me on into a deeper gameplay experience. I made it across the line with about a tenth of a second between me and Bowser, who was pushed into second place.
Burcombe also reveals that Super Mario Kart's combat system had a massive impact on WipEout:
The mechanics of Super Mario Kart were virtually flawless, so it was a constant source of inspiration for me. But we obviously couldn’t have banana skins and shells - we had to make it all futuristic and introduce things like electro-bolts and all that kind of sci-fi stuff.