Even though game of dice is such a shame, why was it a rule for the Kshatriyas not to reject invitation for the of dice? Does it mean Yudhistira was under the influence of kali, accepted invitation for game of dice against the advice of Vidura, his brothers, wife who discouraged him to accept the invitation for game of dice?
All the bad consequences happened during Mahabharata, Let it be Abhimanyu's death, Draupadi vastraharan (disrobing). Were all these due to the influence the Kali?
Well as mentioned in the comments with the passing of each Yuga there is a general degradation of the morality however Kali and Dvapar have worked in cahoots before so I wouldn't discount the possibility of what you are suggesting.
The evil-minded and wicked king Duryodhana, the destroyer of the fair fame of the Kurus, was born of a portion of Kali on earth. He it was who caused all creatures to be slain and the earth to be wasted; and he it was who fanned the flame of hostility that ultimately consumed all. They who had been the sons of Pulastya (the Rakshasas) were born on earth among men of Duryodhana's brothers, that century of wicked individuals commencing with Duhasasana as their first. And, O bull among the Bharata princes, Durmukha, Duhsaha, and others whose names I do not mention, who always supported Duryodhana (in all his schemes), were, indeed, the sons of Pulastya.
The Mahabharat thus clearly states that it was Kali in the form of Duryodhan who fanned the hostilities and caused the death of thousands of creatures.
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