Exactly that. That their worldview is informed by a Western perspective. It doesn't say much else, so "Western" only has limited, contextual value as a description.
The same can be said for other descriptions like "Christian," "communist," and "atheist." Interestingly, one person can be a Christian atheist and a communist at the same time. They could be a cultural Christian invested in Jeffersonian or Jesusist philosophy who, despite lacking a belief in God, is still invested in the Christian church community and believes that the church would make a great starting point for forming a communist dual power structure, for instance.
Which part of their worldview is most relevant to describe depends a lot on the conversation. If they're in an interfaith dialogue with a Muslim, they might focus on their Christianity. If they're in a theological debate with other Christians, they might focus on their atheism. If they're trying to organize a political protest, they might focus more on their communism.
And with other Christians, they might distinguish themselves further. Are they Orthodox, Catholic, or Lutheran? With other communists, likewise, they might distinguish themselves as an anarcho-communist or a Marxist-Leninist.
It really depends on what feature of their worldview is most relevant to a given topic. Some facets of our worldview we can't really help, such as our sex, ethnicity, where we're born and raised, the income status we're born into, and so on. We can choose to expand our horizons by listening to the perspectives of people from other backgrounds in order to reduce this uncontrollable source of bias, but we will still usually retain some elements of our background.
Worldviews are dynamic and nuanced. A single label can't tell you everything about a person's worldview, but it can act as a rough estimate that's precise enough for specific conversations.