How can this be, you ask? How is it possible that such a slow-moving exercise can be a martial art? One answer is, moving slowly trains you to move quickly. Tai Chi is a very precise art, involving highly coordinated movement. Doing the form quickly is not helpful in achieving the level of coordination necessary to perform Tai Chi in a martial context. Crucial details get lost.
Another answer is that the postures have martial applications. All that is needed is a teacher who knows them and can explain them well. Some of them are obvious, like a punch or push. Some of them are not, like “prepare for ward off left”, or the “withdraw after punch”. A skilled teacher can give you a wide assortment of attacks and defenses, some obvious, some not, from the Tai Chi form.
What is needed is for you to practice your form first, and as you do, work these techniques, the obvious and the not, into you body through daily practice. Then be instructed in, and play, Push Hands, so that you can learn about balance and body dynamics through a sport application (in the same way that many Ju Jitsu poeple practice their throws in the sport of Judo so that they can gain expertise against a knowledgeable and resisting opponent).
After learning those skills in your Push Hands, it will naturally turn into a martial art, as these skills translate well into the martial arena. Of course if you already have a martial art, these skills will improve what you are already doing. If you do not have any other martial skills, Tai Chi will provide them.
However, it should be stated, that not everyone who practices Tai Chi is practicing a martial art. The vast majority are practicing Tai Chi for its meditative and health benefits, and quite frankly, just because it feels good.
And, simply practicing Tai Chi does not make one a martial artist, even though the fundamental principles are there. One needs to study it for its martial aspects. With an appropriate teacher you can learn things in Tai Chi form that are developed and showcased in the Push Hands: softness, yielding, pushing, pressing, rooting and neutralizing to name a few. Then these attributes will become a potent martial art.