It's been a while since I've played games on devices other than phone or tablet. However, I do have a transient multi-monitor setup. Most programs seem to do the following:
Have options that are flexible enough to handle whatever the user might want. Here are the options from GIMP.
- (checkbox) Save window positions on exit.
- (checkbox) Open windows on the same monitor they were on before.
- (button) Save Window Positions Now.
- (button) Reset Saved Window Positions to Default Values.
Attempt to open with the specified size and position. If it is not possible (screen is not available), use standard defaults.
If there is only one screen available, the application should open on that screen. It's not only unnecessary, but potentially harmful, to display any messages. Users don't need to be notified because they can plainly see for themselves, and showing unnecessary alerts trains them to ignore important ones. (This is not to say that the event shouldn't be noted in a log file somewhere for later review.)
Depending on operating system, more nuanced behaviors may be configurable through the window manager. On some systems, the window manager may attempt to put windows where there's "space" to avoid overlapping windows. If suitable options are not built into your OS, there may be an app to control window placement more to your liking.
On my computer, everything opens on the primary screen, and I move them with a keyboard shortcut, which is much less tedious than dragging windows around.