Yes and No. And yet your Martial art can either have Kung Fu or not.
Technically speaking, the term "Kung Fu", sometimes spelled Kongfu or Kong Fu, comes from the Chinese words 功夫 (gōng fu), and means skill, art, labor, or effort. Put together it means a skill or art derived through labor and effort.
Personally, I like the general understanding of Kung Fu as a "Skill derived from hard work". But whatever the definition, martial, defense, fighting, etc., are not even hinted at in the literal translation. So then, a chef, a painter, a professional speaker, an athlete, and yes, a martial artist – can all have kung fu…Or not.
If they haven’t gone through serious training and intensive effort & labor, then most likely none of them will have kung fu.
The direct translation of Martial Art into Chinese is actually 武術 (wǔ shù), as wushu, martial arts such as shadow-boxing, swordplay, etc. Martial artists do martial arts, known as wushu, and yet they may not have kung fu. Sounds silly, but it’s beginning to make sense, isn’t it?
But wait a minute; I thought wushu was the acrobatic, gymnastic and aesthetic sport? And Kung Fu was the traditional Chinese martial art… Again unfortunately, yes and no. These terms and their associated meanings have come about due to a bit of confusion on the above definitions over time.
Wushu, as a competitive sport, originated from the traditional Chinese martial arts, and has grown and evolved to become its own culture, activity, and yes, kung fu (for some). Usually to differentiate, some might call this "Contemporary", "Compulsory", "Sport", etc. "Wushu", while calling the traditional Chinese martial arts "traditional", "Kung Fu" or simply by using the actual style name, (although this can be confusing as some contemporary wushu forms use names that are the same as traditional style names!).
Kung Fu as a Martial Art
Although I’m not sure of the origin of the misnomer, badly translated and dubbed versions of phrases like "You have good skill" in Chinese action movies, a certain television show, and now the all-famous movie Kung Fu Panda, sure don’t help in understanding the real meanings of these terms.
So although technically speaking Kung Fu is not a martial art, more generally speaking it refers to the diverse families of traditional Chinese martial art styles, and although wushu technically means martial art, in general people will use this to refer to compulsory or contemporary sport wushu.
Regardless, whatever art you choose – whatever is "your thing" – develop your kung fu!