Hello Redcup,
Most employers are familiar with and prefer the chronological format in CVs. It's easier for them to peruse it. Resumes are more scanned than read.
When applying to Japan, it's important to remember that some employers may not be completely fluent in English themselves. It'd be prudent to give them the easiest, best-known format to follow.
Many people applying for jobs in conversation schools for the first time are new grads or out only a few years. Don't worry about your jobs, just list them along with your education. Any kind of connection to teaching -- private tutoring, volunteering with children or adults -- certainly helps if you have no formal experience.
Your real estate experience involves a lot of public contact, right? You're already used to working with people and that's important. It might help to include a small section on top listing your skills and people-related accomplishments.
But again, keep it simple. Remember, many reading it will not be native English speakers themselves. Also important -- some schools in Japan will accept American-style resumes (my first one did); others insist on the international CV format which includes personal info such as date of birth, marital status, nationality and a photo. This is typical around the world.
Best of luck!