Using a phone while it charges with a quality, certified charger and cable is largely safe by today's standards. Modern phones and chargers include protection circuits designed to manage the extra heat and current variation that comes with active use during charging.
The real source of risk is usually product quality; a fake or uncertified charger may not safely manage the extra electrical load created by active use. Most of the 'phone exploded while charging' stories that circulated in the past have been traced back to low-quality or damaged products of this kind.
Demanding activities like gaming can raise phone temperature from both the processing load itself and the charging process combined; in that case, performance may throttle automatically as a safety measure, not a malfunction.
Using a thick case while charging makes it harder for heat to escape, which can both hurt performance and theoretically raise the risk of overheating; removing the case is a sensible precaution if you plan on heavy use while plugged in.
In the end, when using CE-certified, protection-equipped products from a trusted brand like Charjett, using your phone normally while it charges is not a practical concern in everyday life.