A gym, short for gymnasium, is an open air or covered location for gymnastics and athletics and gymnastic services such as in schools and colleges, from the ancient Greek gymnasium
That being said any activity done in these perimeters counts as gym, so the shirts don't lie. Gym life is subjective and defined by the user. Some peoples gym life includes only cardio, some only weights, some a mix, some boxing/mma, etc. Personally I'm not going to walk up to a heavy weight mma champion and tell them they aren't about the gym life if they mainly do cardio, cause it isn't my business to say "hey, you don't do the things I DO, so that means you are not about the gym life". Pushing your agenda on others wouldn't make them douches, but the person in the mirror.
Honesty I don't worry about others and focus on my ****. Let them think what they want and believe what they believe, got too much on my plate to worry about peasants