Section 1 of Article I of the New York Convention sets two criteria to identify a “foreign arbitral award”, arbitral award “made in the territory” of another State and arbitral award “not considered” as domestic award. However, only the first criterion has been used for many years as a result of the “Notice of the Supreme People’s Court on Implementing the Convention on Recognition and Enforcement of Foreign Arbitral Awards to Which China Has Acceded” on 10 April 1987. According to this Notice, the Convention is only applied to the recognition and enforcement of foreign arbitral awards rendered in the territory of other contracting states, and with regard to the awards rendered in the territory of non-contracting states, the relevant provision in civil procedure law[1] is applied (explanation about the reciprocity reservation that China has made). This Notice didn’t mention the second criterion because it’s too ambiguous and difficult for the local courts to apply.
The case you mentioned is the first case that the People’s Court use the “non-domestic award” criterion, but this court is a local Intermediate People’s Court, and doesn’t have enough influence to establish a new criterion or rule to determine which award is a Convention award.
Actually, sometimes the judges including judges of the Supreme People’s Court were considering using the second criterion, but they didn’t file a ruling based on it. Maybe in the future, the Chinese courts will use both of the criteria; it depends on the opinion of the Supreme People’s Court.

Ⅱ. The rule of the applicable law to the arbitration agreement can be learned from related Interpretation.

In different cases, the results may be different. The mystery is the applicable law to the arbitration agreement.
Article 16 of the “Interpretation of the Supreme People’s Court on Certain Issues Relating to Application of the Arbitration Law of the People’s Republic of China” stipulates the rule of the applicable law to the arbitration agreement:
In the examination of the validity of foreign-related arbitration agreements, the law agreed by the parties shall apply; where the parties have not agreed on the applicable law but agreed on the place of arbitration, the law of the place of arbitration shall apply; where neither the applicable law nor the place of arbitration is agreed, or the agreement on the place of arbitration is not clear, the law of the place where the court is located shall apply.
If the parties want to use foreign institutional arbitration in China, the best way is to choose a foreign law to govern their arbitration agreement. Then the Article 16 of Arbitration Law[3] will not be applied.

[1]The notice mentioned Article 204 of the Civil Procedure Law of the PRC (for Trial Implementation) (the “Trial Civil Procedure Law”), which was adopted by the Standing Committee of the National People’s Congress in March 1982, and substituted by the 1991 Civil Procedure Law. According to Article 204 of the Trial Civil Procedure Law, the provisions of international treaties and the principle of reciprocity were two bases to enforce foreign awards. These two bases were followed by the 1991 Civil Procedure Law.

[2] “Interpretation of the Supreme People’s Court on Certain Issues Relating to Application of the Arbitration Law of the People’s Republic of China”, Fa Shi [2006] No. 7, passed by the 1375th session of the Judicial Committee of the Supreme People’s Court on 26 December 2005, promulgated on 23 August 2006.

[3] Article 16 of Arbitration Law:
An arbitration agreement includes an arbitration clause included in a contract, and an agreement on submission to arbitration in other written forms concluded before or after the dispute arising.
An arbitration agreement shall contain the following particulars: (1) an express of the intention to arbitration; (2) matters for arbitration; and (3) a designated Arbitration Commission.