The game appears to be from the 2000s, as its graphics and game design resemble games from that era. The monitor of the arcade cabinet does not appear to be a CRT monitor, which further supports this idea. The game features a minimap, and the player appears to be competing against a red transparent "ghost" car, which may be a recorded run or a computer-controlled opponent.
The arcade cabinet and in-game banners bear the label "Rally Ridin'," but there appears to be no arcade racing game released under that title. I'm wondering if the arcade cabinet is a fake, but perhaps the game itself was based on a real racing game. It's possible that the creators of Poker Face took the "Rally Ridin'" name from the in-game banner signs of an actual game or maybe edited those signs in and used the same name to label the fake arcade cabinet.
As commented by @JourneymanGeek, it seems that the "Rally Ridin'" arcade cabinet is based on the Nascar Racing arcade cabinet. The designs are strikingly similar, and the "82" marking has even been retained in the "Rally Ridin'" arcade cabinet. However, the game itself seems to be different from the Nascar Racing arcade game.
Image source: arcadeclassics.com.au