If the people who become infected with the coronavirus but recover from COVID-19 can get reinfected, does this mean exposure to the virus confers insufficient immunity? And does that in turn imply a vaccine has little chance of preventing future spread of the virus?

Unfortunately, this is exactly the correct interpretation to take. Your intuition is serving you well here to understand this is a horse of a different color, so to speak, it is more akin to the HIV virus in its mutation potential. This will create great difficulty in achieving a universal vaccine that will be effective as a countermeasure, because of the changes in the virus occurring so rapidly it will become invisible to the vaccine as soon as it is ready on a large scale, and then will have no benefit. By the same token, those immunized will be immunized against last month’s virus and not the current one spreading continually through the population, so it will prove to be a futile exercise in the end, much as with the common cold.