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Digital platform economies have restructured contemporary markets by shifting economic coordination from decentralised exchange toward algorithmically governed systems of visibility and participation. Although prior platform economics literature has primarily emphasised network effects, switching costs, and informational asymmetries as separate drivers of platform dominance, less attention has been given to their systemic interdependence within platform infrastructures. This study conceptualises platform economies as recursive systems comprising structural mechanisms and market outcome structures that co-evolve through reinforcing feedback loops. The structural system includes network effects, switching costs, informational asymmetry, two-sided market dynamics, and algorithmic governance intensity, while the outcome system consists of platform market power, market concentration, visibility allocation efficiency, transactional dependency, and consumer welfare outcomes. Platform dominance is theorised as an emergent property of these interacting systems rather than a function of isolated causal variables. Using Canonical Correlation Analysis on survey data from 308 active platform users in South Africa, the study identifies a strong and statistically significant multivariate relationship between structural mechanisms and market outcomes. Algorithmic governance intensity and network effects emerge as the most influential structural drivers, while platform market power and transactional dependency dominate the outcome structure. The findings further indicate a structural shift in platform power formation, where algorithmic governance increasingly supersedes scale-based explanations rooted in traditional two-sided market theory. However, consumer welfare outcomes exhibit a weaker and negative association, suggesting that intensified infrastructural coordination may coexist with reduced perceived autonomy and fairness. The study concludes that platform economies operate as recursive coordination systems in which algorithmic infrastructure, dependency formation, and market concentration mutually reinforce one another, positioning platform power as an infrastructural rather than purely competitive phenomenon.