What do you call the part in game screen that shows information about the current game (like money, health point, time left, time elapsed, ...) ? Thanks

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HUD is heads up display

GUI is graphical user interface

gauges, meters, indicators, character info, and level info are all relevant terms.

The term "status panel" might fit for the indicated GUI element, I think.

I would go with info or status panel for the highlighted section, or [something] panel if you can come up with a more specific term related to the information displayed in them. (Budget/Accounting/Heath/etc, depending on what kind of info is displayed in such a box, and whether or not there are different boxes showing different kinds of information on screen.)

HUD is a bit of an abused term at times these days. Specifically a "Heads Up Display" is a look-through or 'near-edge' kind of thing where the user can switch focus between the info presented in a transparent display and the 'world' around them without actually having to take their eyes off the world itself.

Back when a 'huge' monitor was a 14" CRT then elements near the edges of the screen were easily used as part of a HUD setup. They made sense to consider that a HUD design because the screens were so small that there was no real eye deflection to see them, and you could focus on the info and the world at the same time. However having played games on 30"+ screens and multi-monitor setups, I have to say that frequently those GUI elements around the edges of the screen really are no longer fitting of the "HUD" concept in many cases, and game designers should really keep that in mind when they are deciding how to present information to their players.