Your intuition is correct. The sentence should be:
{Name of the competitor} had the lowest price on the market...
Usage is idiomatic. "The market" isn't referring to a physical marketplace such as an open-air fish market, or a farmer's market. Instead, it is an abstraction, like an economic market, and may refer to automobiles or housing.
Usage is slightly different if the market is financial, such as a stock or commodities market.
- Buying and selling of stocks refers to "the stock market". A particular, but still abstract, instance is "the European stock market".
- A named market is a proper noun, often a physical entity, such as the Paris Bourse or the London Metals Exchange (LME). Virtual markets are markets too. The NASDAQ is an all-electronic exchange. Bitcoin is too.
- "Commodity" is used as an adjective to describe the type of market e.g. platinum options are traded on a commodities market such as the Chicago Mercantile Exchange (CME) or the LME.
Pork bellies are traded on an agricultural exchange (market). Pork belly futures are listed by, or on, the CME. The traders themselves are in the market to buy or sell pork bellies. That is metaphorical too. It doesn't describe location, but rather, intent to act. If the traders were on the market, then the traders themselves would be bought or sold! Very meta, to trade traders, and wrong, as traders aren't chattel.
Summary
One takes one's pigs to market, sells them in the marketplace, offers them as listed futures on a commodities exchange, and sells them to the highest bidder on the market.