On arrival in Japan under the current COVID conditions, how does one go from the arrival gate to one's vehicle?

The answer that you do, indeed, simply walk to your vehicle. The regulations prohibit using public transportation, but place no further requirements on private transportation.

More generally, Japan being an orderly society, COVID regulations are not enforced at gunpoint, you are simply expected to do the right thing. You are required to sign a Written Pledge on arrival at the airport where you promise to do so, and if you fail to do so and are caught, consequences may include detention and, for foreign nationals, deportation:

From January 14, 2021 until further notice, all Japanese nationals and foreign nationals with the status of residence are also required to pledge to refrain from using public transportation, and to be in quarantine at home or other designated areas, retain the location data, and provide it to the health centers or other institutions, if requested. (If separate quarantine measures are to be taken, those also need to be pledged.) They are required to sign and submit the Written Pledge when entering Japan. In case of violation, they may be subject to detention under Quarantine Act.