Is the -ing a participle in the sentence?

Solution 1:

No, it's a gerund.

In the example

"The president of the World Bank says he has a passion for China, which
he remembers starting as early as his childhood."

The NP object of "remembers" is "(it = which) starting as early as his childhood", and this is a nominalization of the sentence "it (the passion) started as early as his childhood". The -ing form of a verb in a nominalized sentence is called a "gerund", as I understand the terminology.

Solution 2:

The president of the World Bank says he has a passion for China, which he remembers starting as early as his childhood.

The relative clause is "which he remembers ___ starting as early as his childhood", where gap represents the NP antecedent "a passion for China". "Remember" is a catenative verb, so this is a complex catenative construction in which the intervening NP "his passion for China" is object of “remember” and the gerund-participle clause "starting as early as his childhood" is catenative complement of “remember”. "Starting" is a gerund-participial verb-form; it heads the catenative complement clause. The preposition phrase "as early as his childhood" is a temporal adjunct modifying the VP.