Yes, boxing is a martial art.
Modern standard western boxing has limitations, for example, rules dictate that you can’t grapple, or strike with anything but the fists, you must wear well padded gloves, and you must fight from a standing-up position; however, the skills that boxing does focus on are integral to any strike-style martial art like Karate or Kung Fu for example.
Some martial arts focus on striking (like Karate) while others focus on grappling (like Judo). Western Boxing is one that focusses specifically on striking, more specifically on striking with the fists, but this hyper-niche focus by no means stops it from being a martial art.
Some people say that Karate can be practised as a sport or as an art – when pracitised as a sport it’s all about scoring points in competitions (bound by rules) and when practised as an art it’s all about humbly refining the skills that would be too dangerous to use in a sport. However, even UFC MMA is bound by the rules of their sport (no kick between the legs for example) and this creates a lot of wrestling-style stances that would easily be defeated by a kick between the legs, but nobody denies that this is still a martial art. So it’s safe to say that Boxing is a martial art, with limitations, and when practised side-by-side with other martial arts can be a great training supplement for serious martial artists so long as they appreciate that when trained with a point-scoring approach this way would not be so practical in a real fight with the sport’s rules removed. At the higher levels of boxing much of this is well known – Jack Dempsey wrote about it in 1950. And at the highest levels of karate & kung fu, your punching involves all the same jabs, hooks, uppercuts, blocks, parries, evasion, defensive structures and footwork as you’d see in the elite levels of western boxing.