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I did not like the examples. They made me believe that the author doesn't have a good grasp on the concept of "infinite." For examples:

"The king’s worth, therefore, cannot be bound within a finite set of values."

There's no reason to say that the king has an "infinite score". Nothing would change were the score equal to all of the other pieces of the game combined, plus 1.

"More importantly, philosophers, religious scholars, legal experts, and ethicists often assign an infinite value to human life."

We observe in real life that this isn't true. We send people into space when we know there's a non-trivial chance (~0.5%) that they will die. If we assigned an infinite value to their lives then we would never do that.

There would be no difference if "infinity" in this case were synonymous with "all the wealth in the world."

"And therein lies another kind of infinity: death. Assuming that nothing awaits us in the afterlife, the termination of our lives represents a kind of eternity."

This logic is inverted. Lives are finite. If time continues forever then the complement of "finite" (to cover the period when someone is not alive) is indeed infinite ... in the same way that the termination of 9 July 1904 is also a boundary between a finite time range and a hypothetical infinite time period.