what is the right way to describe busy person that love do other things

The question is rather nonsensical, but let's start by correcting the question as you asked it:

"What is the right way to describe, in three (in English usage, numbers of ten or fewer are written out rather than using the numeral) words or fewer (if you can count individual units, such as words, you say fewer, not less), someone who ("person which" is really bad English--there was no article before person, and which is for things, not people; someone avoids the problem of an article, and who is used for persons) is very busy in life, but loves (verbs must agree in number with the subject--the subject here is third person singular, so there is an "s" at the end of the verb in the present indicative) to play casual games.

What is the right way to describe, in three words or fewer, someone who is very busy in life but loves to play casual games?

Now, the question is nonsensical for two reasons. First because you assume that busy automatically implies that one is "busy in life" (an awkward locution which is not typical English usage). The second reason is that you assume that there is a single word in English which unambiguously means "busy in life." there is none that i have ever heard of. To express this idea, you'll have to explain each separately--that the person in question leads a busy life, and also likes to lay casual games. (If someone is so damned busy all the time that it characterizes the person's life, when do they have time to play casual games?)

It reads as though you are trying to write a personal ad for a dating site: "Casual gamer, very busy most of the time, with little time to spare, seeks woman with low self-esteem for hurried, loveless sex."

They are called a productive, eclectic gamer.

For general writing, most guides agree that you should use words for the numbers one through nine, but for larger numbers the rules vary wildly from style guide to style guide. The Chicago Manual of Style recommends spelling out the numbers zero to one hundred and using figures thereafter — except for whole numbers used in combination with hundred, thousand, hundred thousand, million, billion, and beyond (e.g., two hundred; twenty-eight thousand; three hundred thousand; one million). The Guardian says one to ten and figures thereafter. Whatever style one chooses, one 'rule' that everybody can agree on is: be consistent.

A golden comment.
Our dear veteran Set often deals with semi-sane newbies.