The simplest ways of narrowing down your selection process are the bare necessities. When you say "not too big of a size", it can mean the thickness and the width/height. Width/height is usually dictated by the screen size. For great portability, 14" screens are great, 16" are good, 17" or 18" is probably not very portable for a child. The lighter and more portable the computer, the less you can fit on the screen and less performance you have so it is always a balance of what you need more.
For the games mentioned, genshin, counterstrike, you do not need a top of the line model, these games are not very demanding. That is a good thing because even 2023 and 2022 models can do the job and you may find some excellent deals on those. Unless you are looking at an ROG tablet computer, I believe they all that a dedicated graphics card so graphics performance should not be an issue. This you can always check at the store if you have doubts, but if the product details mention NVidia, you know it has a dedicated card. There is an option to have an AMD dedicated graphics card, but you have to be careful not to confuse it for an AMD processor (NVidia does not make laptop processors, but AMD does; ROG generally favours NVidia anyway). The graphics card choice and how each different model is configured is usually a contentious point for people who want to get the absolute most out of what they pay for, but there are many details to check on every model and to be frank, as long as there is a dedicated card, the needs you mentioned should be satisfied with some headroom for more demanding tasks and games in the future.
For video editing and making sure the laptop can be used for a long time, I would say the easiest thing to check is the amount of RAM. It may be upgradeable, but I would still recommend 16GB of RAM at a minimum. Not to be confused with DRAM (usually mentioned at the graphics card) or other storage measurements (SSD, HDD).
For something simple that should last a while, the G14 and G16 (14" and 16" respectively) are decent options. The ROG Strix line is a little thicker, but can also be worth a look.
