If the reality is as mentioned, the money this man paid to the solider is a bribe that should not have been paid. On the other hand, kissing Al-Hajar Al-Aswad is an act of Sunnah (supererogatory act of worship following the example of the Prophet); not one of the rituals of Hajj. Thus, it becomes Mustahab (desirable) for anyone who is able to reach it to kiss it as long as they do not harm others. However, if it is difficult for some to do this, it is sufficient for them to touch Al-Hajar Al-Aswad with a stick and kiss it. If this is also difficult, the person who circumambulates could just point at Al-Hajar with their hand when they pass by it, and say Takbir (saying: "Allahu Akbar [Allah is the Greatest]"). This is in accordance with the Sunnah.
Giving bribes is not permissible for a person who circumambulates and likewise it is not permissible for a solider to accept bribes. They both committed a sin from which they have to make Tawbah (repentance to Allah).May Allah grant us success. May peace and blessings be upon our Prophet Muhammad, his family, and Companions.