puzzling used in this way would be a gerund. gerunds are derived from a verb X and take the meaning of "the activity of doing X".
reading is derived from the verb read, and it is clear that the gerund does mean the activity of this.
gaming, on the other hand, doesn't work like that, because the verb game means to gamble (it can also mean to cheat the system). The gerund gaming therefore means the activity of gambling. When gambling started to get automated in 1891, machines where you put money into a slot and pull the handle were called gaming machines.
In the 1970's, the first computerised games were installed alongside the slot machines, and so the activity of playing computer games became known as gaming even though in most computer games at the time no gambling took place. Because of its origins, gaming has a specific meaning (computer games) rather than the general meaning of playing any kind of game.
With puzzling, the verb puzzle has this definiton in the Cambridge Dictionary.
to cause someone to feel confused and slightly worried because they cannot understand something, or to think hard about something in order to understand it
The natural meaning of puzzling as a gerund would therefore be the activity of confusing people.
That said, nobody controls the English language, so you are at liberty to create neologisms for your personal use or for humourous effect. If the english-speaking community feels the need for the word you create and likes your neologism, it could one day end up in the dictionary.