The world's languages exhibit certain so-called typological or implicational universals; for example, Subject-Object-Verb (SOV) word order typically employs postpositions. Explaining the source of such biases is a key goal in linguistics. We study the word-order universals through a computational simulation with language models (LMs). Our experiments show that typologically typical word orders tend to have lower perplexity estimated by LMs with cognitively plausible biases: syntactic biases, specific parsing strategies, and memory limitations. This suggests that the interplay of these cognitive biases and predictability (perplexity) can explain many aspects of word-order universals. This also showcases the advantage of cognitively-motivated LMs, which are typically employed in cognitive modeling, in the computational simulation of language universals.