Cognitive accessibility in video games remains one of the least explored and most challenging areas to address, as the target audience comprises a diverse group, including individuals with cognitive disabilities, but also learning difficulties. To gain deeper insights into how cognitive accessibility in video games could be improved, and due to the wide array of potential users, we conducted a study with persons with dyslexia, since this learning difficulty has not been examined in detail in the existing literature on game accessibility. Two focus groups were carried out to elicit information about the experiences of people with dyslexia in relation to video games, focusing on the barriers that break immersion and hinder the physical and emotional experience of gameplay. Thematic analysis was used to interpret the results. Findings suggest that while video games can offer enjoyable and immersive experiences, they may become alienating if not fully accessible. The main barriers preventing the participants with dyslexia from fully immersing themselves in a video game are reading, memorizing information and controls, and keeping up with the pace of the game. Particularly, they encounter difficulties with heavily text-driven games, and consequently prefer action games or those with a faster pace. In the conclusion, we lay the groundwork for a future reception study aimed at overcoming these barriers to foster more immersive game experiences.