The Drag Store owner runs a drag racing store for racing fanatics who specifically love drag racing, also known as Zeroyon. He allows the protagonist to choose a time trial drag race at zero cost. The challenges he holds are the Normal Drag, Water Drag and Aqua Drag in which may or may not need specific parts to have an efficient time.

The Normal Drag requires parts to provide the protagonist the most acceleration and speed.

Unlike the Normal Drag, the Water Drag occurs on the water's surface, thus in addition to requiring parts good acceleration and speed, it is mandatory to equip the Ship Bottom or Hovercraft in order to participate.

Similar to the Water Drag, the Aqua Drag occurs under the water thus in addition to requiring parts good acceleration and speed, it is mandatory to equip the Submarinder in order to participate.

Trivia

This individual has the same color scheme and body and drag racing-related interests like Johnny from Choro-Q HG 2, or in reality...could it be Johnny?
In the Japanese release, the Drag Store is known as "ゼロヨン受付" (Zeroyon Reception). Zeroyon is a term for street races that take place in industrial areas and on straight roads.
There appears to be unused dialogue found within the game files.

When searching through the game files, the Drag Store Choro-Q appears to have unused dialogue that does not appear anywhere in the game. Upon arriving to Noise City, you can participate in the mini-games that the Drag Store provides right away. While you can only access Noise City by obtaining 11 Flags, using the debug mode to reduce the amount of flags shows that there is no criteria that you must hit in order to participate in the Drag Store's mini-games. Thus, the dialogue is unused.

"Hello! We're not open yet. We'll be open in the near future, so visit us again soon!"

Game Dialogue

General Dialogue

Default Dialogue

"Hey! This is a drag racing store just for us racing fanatics. If you love drag racing, we'll challenge you at no cost. Would you like to challenge?"

(No!): "Please come visit again!"

(Yes!): "Please select what would you like to do."

(Normal Drag): "Normal Drag, Let's go!"

(Clear/Tie):"Thank you very much. Next time, let's try harder and beat the record! One more time... Would you like to challenge?"

(Record Broken): "Wow! You're great! You've set a new record! One more time... Would you like to challenge?"

(Retire):"You're going to quit already? Or... Would you like to challenge?"

(No!): "Please come visit again!"

(Yes!): "Please select what would you like to do."

(Water Drag): "Water Drag, Let's go!"

"You cannot enter the race with your current equipment. Please equip the Hover or the ShipBottom in the garage."

(Clear/Tie):"Thank you very much. Next time, let's try harder and beat the record! One more time... Would you like to challenge?"

(Record Broken): "Wow! You're great! You've set a new record! One more time... Would you like to challenge?"

(Retire):"You're going to quit already? Or... Would you like to challenge?"

(No!): "Please come visit again!"

(Yes!): "Please select what would you like to do."

(Aqua Drag): "Aqua Drag, Let's go!"

"You cannot enter the race with your current equipment. Please equip the Submarinder in the garage."

(Clear/Tie):"Thank you very much. Next time, let's try harder and beat the record! One more time... Would you like to challenge?"

(Record Broken): "Wow! You're great! You've set a new record! One more time... Would you like to challenge?"

(Retire):"You're going to quit already? Or... Would you like to challenge?"

(No!): "Please come visit again!"

(Yes!): "Please select what would you like to do."

(Hear explanation): "Normal Drag challenge is to see how fast you can finish a quarter mile on a regular road course. There are no limits on parts. Water Drag challenge is to see how fast you can finish a quarter mile on top of water. You have to have either the Hover or the ShipBottom to equipped to enter this race. Aqua Drag is a challenge to see how fast you can finish a quarter mile underwater. You have to have the Submarinder equipped to enter this race."

(Maybe next time): "Please come visit again!"