Yes, they are wired in series and you are right that for this project a parallel circuit would work better. For a large project though, where you would have multiple strings, parallel circuits are not ideal. From what I was told, if you connect a few parallel strings together on a driver (a larger driver than used here, like a meanwell type driver) and one LED fails, it will overdrive the other string and probably fry all of the LEDs on the other string. I'm just an amateur at this and really don't know everything, I'm just following what I've read.
Wiring the leds in parallel with each other would put 15 volts across each LED which is not ideal considering they are run at a max of 3.75 volts. Also the current would not be enough as you would need way more than 1amp. Just remeber that in a parallel circuit that voltage always stays the same and current changes, and in a seires circuit the current is always the same and the voltage changes.
You would not want to be put more than 1 string of leds on single driver, as you do run the risk of overdriving the other leds, as you mentioned.