Comment by Fnoord

Ah yes, the game I know as 'pictionary'. There used to be an implementation of this on a website using Macromedia Shockwave. You'd have public rooms where you could start guessing. The person with most points would be next drawer. It was fantastic in start, but also a place where young kids would play, and some let us just define them as older kids who would ruin it by doing things like drawing dick pictures. Eventually, nobody would use Shockwave anymore, and you wouldn't even want to run such in a production environment anymore.

As for the name, boompje means little tree (kleine boom) but boontje means little bean (kleine boon) and koninkje means little king (kleine koning) but little queen would be koninginnetje (kleine koningin), and finally hoopje would mean little hope (kleine hoop). So while -tje is default, there are variations. If the word ends with -m, you do -pje. In this case, we have a word derived from English (game) and we need to use the way it sounds (geem) hence geempje (gamepje).

For a foreigner dealing with The Netherlands and Dutch, gametje sounds cute. It fits the role, so to say. In multiple ways. This is a kids/family game, and kids make simple mistakes in grammar when learning their native language, like adult foreigners do when learning a new language. The earlier mentioned website (I forgot the name, something like iSketch? Yes that was it [1]) existed before emoji were a thing. You'd have emoticons but not as part of a font , unless you count say wingdings or using (foreign language) symbols like :-) and more complex ones such as ¯\_(ツ)_/¯

[1] https://en.wikipedia.org/wiki/ISketch