The day at a glance calendar system used in this Orient watch, has been used in a number of watches over the past 40 years, perhaps most famously in the Wittnauer "2000" watch (which Orient actually made for Wittnauer under contract). Orient itself has used this system in a number of different styles of watches. Note that the daily date window is separate from the day of the week / month at a glance system; the date window is driven in traditional fashion by the movement.
The day/month at a glance system is based on a single disc inside the watch that is manually advanced by the user. If you look at the top of the watch, where the months are listed, you'll see little two-digit numbers. These represent different years--"04" refers to 2004, "11" to 2011, etc. To get the right days of the week at the bottom of the dial, you move the appropriate year under the current month. That will line up the days of the week--Monday, Tuesday, etc.--with their correct dates. You may see the same year repeated more than once on the upper part of the dial because the calendar has a specific pattern that can be replicated.
On older watches using this same system, the top pusher was used to adjust the date window, and a separate winding knob controlled movement of the year/monthly calendar disc. On this specific watch, which I have not handled in person, I cannot see a separate crown to adjust the date, and so I am guessing that you would pull out the set stem part-way to engage the disk setting mode. This would make sense because unlike the date window, where the date is always advanced, the year must move both backwards and forwards to align with all the months in a given year--you'll see that January and October are in the same place on the dial, for example.
If you're interested, here's an example of a vintage Orient that uses this same system for its calendar. Note how the monthly calendar and year/month alignment are flipped from the watch you asked about. Please note that I have no connection with this web site, make no endorsement as to the price being asked for this watch--but it has a nice picture of a classic Orient:
On a final note, you'll see a number of people refer to these as "perpetual calendar" watches. That's not accurate. The year / days of the week disc holds about 20 years of calendar information. After that, the disc is no longer accurate, though you can easily keep aligning the monthly calendar just be referring to a printed calendar and adjusting it that way. For a period of time (not sure if they still do it), Orient would accept older watches with this system and change out the old year/day wheel with a new one that went further into the future.