One comment says:
The West has been importing Chinese goods from way before 2004. Western companies entered into joint venture contracts as well. These can't have all been state-owned enterprises [...]
Indeed they were not. The source cited by the OP is a bit misleading. Private enterprises had been constitutionally authorized earlier in the PRC (1988), as the source found by origimbo details:
The post-Mao economic reforms saw the emergence of private enterprise, defined as “a privately funded economic entity which employs at least eight persons”. Article 11 of the Constitution was then amended in 1988 to “permit the private economy to exist and to develop within the limits prescribed by law” and defines such an economy as a complement to the socialist public economy. Here, the private economy refers to the economy in the form of private enterprises as defined by law.
And about 10 years later (before the 2002 SME law), the constitution was changed again:
Through the 1999 constitutional revision the individual and private economies were no longer defined as a complement to the socialist public economy; they were treated as “an important component of the country’s socialist market economy”.
What the 2004 revision did was to further remove some "discrimination" against private enterprises:
there is a clear need to accord constitutional protection to these new forms of the private economy, hence the insertion of the phrase “other non-public economy” into Article 11 through the present revision. Though the phrase is an ambiguous one, it is meant to embrace the various existing and emerging forms of private business, including foreign investment in China. In addition to providing protection, the revision further adds that the state will also provide encouragement and support to the development of the non-public economy. By doing so, the private sectors final achieve equal status with their public counterparts in most economic activities.
And not coincidentally the 2002 law was a SME Promotion Law.
One difference that remained though in article 13:
While private property is not deemed sacred, as is public property, it is now declared inviolable. [...] the use of the adjective “lawful” in front of private property is not redundant; it is used to address the fear that illegally acquired property might become untouchable.