Should one start putting in more hours as well, (I always do it when
there is some work that needs immediate attention, and not otherwise)
or should I not bother with this?
Unless this is an hourly job, in every workgroup some folks will choose to work more, while others work less.
If the company culture is such that individuals who complete many more tasks (or even who just spend many more hours) are rewarded, then you need to consider if you want these rewards too, and if these rewards are worth the extra time.
Some company cultures reward a more holistic approach where team achievements are primary. Other company cultures reward individual achievements. Some companies expect overtime work. Others frown on it. No matter what you do, you need to figure out where your company stands on this, so that you can make an informed decision either way.
Only you can know what you should do. Your home situation may dictate your actions. Even if someone else is working 14 hours per day, that doesn't mean your family situation is such that you could do so, even if you wanted to.
And your career situation may help dictate your actions. In some professions it would be expected that long hours are required, where in other professions it would seem odd. And in some careers long hours would be expected early in your career, but not so much later. I have always worked an average of 55 hours per week when I loved the job, somewhat less when I didn't, but always more than 40. That was always my choice, but I also knew that it was a good way to get ahead quickly in some shops. I understood the culture.
Instead of just blindly deciding to put in 14 hours because one coworker does, take some time to think it over. What do your other coworkers do? What seems to be rewarded at this company? And how would 14 hours affect your life outside of work? Most important, do you want to work extra hours to get ahead, or would you rather find a way to get ahead without so many extra hours.
You may choose to work more. Or you may not. Either way can lead to success (although depending on company culture it may take longer, or you may need to find a different company).
(And if, as some claim, working more than 40 hours causes a loss of productivity, then your colleague is already failing in ways that should be obvious to you. Thus you wouldn't want to emulate failure. That doesn't seem to match what you are actually observing, though.)