What is the ruling on supplicating for someone not for the sake of Allah, such that the supplicant stipulates a personal interest to be fulfilled in exchange for the supplication, and does this fall under the category of shirk (polytheism)?

Praying for someone who has done a favor is not showing off (riya'). Riya' is performing an action to please people. However, whoever prays for someone who has done him a favor has obeyed the command of the Prophet, peace and blessings be upon him: "Whoever does you a favor, reciprocate it. If you cannot find anything to reciprocate with, then supplicate for him." Thus, reciprocating with prayer is praiseworthy and legitimate, as is promising to do so. And doing a favor seeking prayer is neither polytheism (shirk (definition)) nor showing off (riya').