If you are a "pretty good chess player" you are most certainly playing with tactics and strategy, you are just not aware of it. Becoming aware of it would make you a better chess player.
I have a friend who got me into the whole chess scene he plays online against computers and online chess players all the time he is not a professional or anything but pretty clever chess player I learned from how to play the game and now I can beat him pretty easily took some time though. But I notice people do things like Queens gambit or other tactics. When I play I play so I don't lose a bishop for a knight basically point based strategy and just try not to get any of my pieces taken out but I've never actually studied any tactics or anything like that maybe I am playing with it just no aware of it.
Using the point system works at a basic level, but beyond that it is not so helpful. A bishop isn't always worth more than a knight, a bishop pair isn't always great, a rook isn't always worth two minor pieces, etc, etc. Knowing how to make these judgments is part of strategy.
