Wikipedia has this to say on the usage of -ing
-ing is a suffix used to make one of the inflected forms of English verbs. This verb form is used as a present participle, as a gerund,
and sometimes as an independent noun or adjective.
The -ing form of a verb has both noun uses and adjectival (or
adverbial) uses. In either case it may function as a non-finite verb
(for example, by taking direct objects), or as a pure noun or
adjective. When it behaves as a non-finite verb, it is called a gerund
in the noun case, and a present participle in the adjectival or
adverbial case. Uses as pure noun or adjective may be called deverbal
Cricket is not usually considered a verb, native speakers won't normally say:"They cricket" or "he loves to cricket" but instead "they
go cricketing", "he loves
to play cricket" or "he loves
playing cricket". Because cricket is already a noun, it's unnecessary to use the ing form when we want to make it the subject of a sentence.
Cricket is played in 104 countries
and when it is the object
He's mad about cricket
In the OP's question, cricketing is used as an adjective, "cricketing nations / terms / shots". Each of these expressions can be searched online.
Footballing is often heard and is a word I'm familiar with in British English, it too is used as an adjective and should be placed before nouns. For example, "Christiano Ronaldo - Footballing Superstar"
In the Cambridge Dictionary it is defined as; relating to or playing football:
It was the high point of his footballing career.
A footballing country/hero
Soccering exists and has earned its place in wiktionary: verb; present participle of soccer. Hence the noun, soccer, is conveniently used as a verb. Online I found several instances of the word used to tag images of children playing soccer.
"This is my friend
Golfing is a noun, verb and an adjective. "I love golfing", "I go golfing at the weekend" and "We went on a golfing holiday" are expressions widely used. Non-golfing in Google books produced a respectable 1,740 results
Chess is a board game, not a sport so I can't imagine it ever becoming a verb in its own right, or chessing even being used as an adjective. You can say someone is "a chess star" and that "he's playing chess later tonight". I can't think of any board game with -ing suffix but possibly tiddlywinking might work!
Kayaking, judoing, basketballing, baseballing, cross(-)countrying, snowboarding, hockeying, etc. all exist with the ing forms and can be used as present participles, as adjectives or non-finitive verbs.
Basically, if you want to add "ing" to any sport or team game there's nothing to stop you, native speakers have been doing exactly that for decades, likewise adding the prefix "non". Some expressions (cricketing and footballing) catch on while others don't. I have yet to hear tennising (?tennissing) or gymnasting but no doubt someone, somewhere, has coined these expressions and I have to admit, I would easily understand their meaning.