Reading research uses different tasks to investigate different levels of the reading process, such as word recognition, syntactic parsing, or semantic integration. It seems to be tacitly assumed that the underlying cognitive process that constitute reading are stable across those tasks. However, nothing is known about what happens when readers switch from one reading task to another. The stability assumptions of the reading process suggest that the cognitive system resolves this switching between two tasks quickly. Here, we present an alternative language-game hypothesis (LGH) of reading that begins by treating reading as a softly-assembled process and that assumes, instead of stability, context-sensitive flexibility of the reading process. LGH predicts that switching between two reading tasks leads to longer lasting phase-transition like patterns in the reading process. Using the nonlinear-dynamical tool of recurrence quantification analysis, we test these predictions by examining series of individual word reading times in self-paced reading tasks where native (L1) and second language readers (L2) transition between random word and ordered text reading tasks. We find consistent evidence for phase-transitions in the reading times when readers switch from ordered text to random-word reading, but we find mixed evidence when readers transition from random-word to ordered-text reading. In the latter case, L2 readers show moderately stronger signs for phase-transitions compared to L1 readers, suggesting that familiarity with a language influences whether and how such transitions occur. The results provide evidence for LGH and suggest that the cognitive processes underlying reading are not fully stable across tasks but exhibit soft-assembly in the interaction between task and reader characteristics.