Older people ageing at the margins (i.e., those experiencing homelessness, incarceration, or persistent poverty) face disproportionately high rates of cognitive decline, yet current screening approaches do not adequately meet their needs. Game-based cognitive assessments (GBCAs) offer solutions but remain untested with disadvantaged older users. This study evaluated ASCAPE-C, a gamified cognitive screening tool of nine minigames co-designed with older people in prison. We assessed usability, acceptability, and user experience with older adults ageing at the margins, and investigated the "failure state conundrum"; the tension between a GBCA's need to create failure states for diagnostic sensitivity and usability principles that minimise frustration. Twenty participants aged 47–92 completed ASCAPE-C and the Montreal Cognitive Assessment (MoCA), followed by a user evaluation survey and semi-structured interview. ASCAPE-C was rated positively for enjoyment (M=4.45/5), engagement, and cultural appropriateness (M=4.90/5), with pacing and instructional clarity as primary concerns. Participants with MoCA<26 reported significantly lower technology confidence (r=0.45) and greater physical difficulty (r=0.42) yet maintained comparable enjoyment. The most cognitively demanding minigame was also the most enjoyed, while a comparably difficult game produced frustration. The critical variable was not difficulty but whether participants understood what they were doing. Three contributions emerge. The "Miyazaki Principle" resolves the failure state conundrum i.e., challenge with comprehension creates satisfaction; without it, frustration. Cognitive impairment and low technology confidence interact to produce unwanted challenge that confounds assessment. Human presence emerged as essential scaffolding, pointing toward conditional self-administration. For people ageing at the margins, these games must be carefully designed and tested with those they are intended to serve.