"exhaustion system" looks like "datsuryoku-kei (脱力系)"

"datsuryoku(脱力)" basically means "exhaused", "lassitude" or "lethargic", but as firecracker has mentioned "easy-going" and "relaxed" fit better.
"system" -> "kei(系)" is used to mean "categolized as some(style)".

I think firecracker has explained very well.

It's like "散歩写真(sanpo-syasin)" - strolling photography, instead of keen street photography. It's not that much arty like Hiromix or Araki. It's just relaxing.
Fujita, Akasegawa, Kuzumi and many other photographers have been proposing that kind of styles.