Bond is trying to escape from Mr. Hinx during the car chase. He attends a Spectre meeting, is outed by Blofeld and then escapes to his Aston Martin under pretty heavy gunfire.
Whilst in the car, he tries to enable several gadgets to aid him in defeating (and potentially killing) Mr. Hinx. However, none of the gadgets work as Bond took the car before it had been fully configured (as it was intended for agent 009, not 007). The only gadget that works is his ejector seat, so he leaves his car and makes his escape.
Whilst you correctly say Hinx will remain a deadly threat to him, so will everyone else at the meeting he encountered (and there were easily a hundred people there). After escaping his car, it plunged into the canal (and no doubt gathered a crowd). It wouldn't have made sense for Bond to return to the scene to shoot Mr. Hinx, likely amidst a crowd of on-watchers, and try to escape. It would be unnecesarily reckless, so he instead chooses to focus on his mission.
One final comment as an aside is related to your final line and what @Johnny Bones says in his comment. Bond in the films is an unusual character. He is usually portrayed as being quite a moral individual, only killing when he has little choice. There are some notable exceptions to this, the most famous of which is his killing of Professor Dent in Dr. No, where he shoots an unarmed man in cold blood.
However, in the novels on which the films are based Bond frequently remarks how extremely uncomfortable he is killing in cold blood.
For example, from Goldfinger:
It was part of his profession to kill people. He had never liked doing
it and when he had to kill he did it as well as he knew how and forgot
about it. As a secret agent who held the rare double-O prefix—the
licence to kill in the Secret Service—it was his duty to be as cool
about death as a surgeon. If it happened, it happened. Regret was
unprofessional—worse, it was a death-watch beetle in the soul.