"The cause" — meaning, the proof — "is only against those who wrong the people and transgress upon the earth without right," meaning: by their disbelief and their denial. "Those, for them is a painful punishment," meaning, one that causes pain.
﴿إِنَّمَا السَّبِيل﴾ الْحجَّة ﴿عَلَى الَّذِينَ يَظْلِمُونَ النَّاسَ وَيَبْغُونَ فِي الأَرْضِ بِغَيْرِ الْحَقِّ﴾ يَعْنِي: بكفرهم وتكذيبهم ﴿أُولَئِكَ لَهُمْ عَذَاب أَلِيم﴾ موجع