Can't exit i3 because no sensible terminal emulator is installed

The i3 environment isn't usable in the case described because there's no way to get to a shell. This is a graphical environment (X also known as X11) running in one of Linux's virtual consoles. To switch to a text environment and get a shell, use controlalt together with a function-key for the number of the virtual console that you want to switch to.

Most X environments with Linux run in virtual console 7, some may be in virtual console 1. So the quickest advice is to choose 2 through 6.

When you do this, you will get a login prompt. This is expected. You can be logged into the same machine several times. Once logged in, you can run pacman to add whatever packages are needed, such as xterm.

Further reading:

• Keyboard shortcuts (Arch wiki)
• 7. Console switching, The Keyboard and Console HOWTO
• 9.2.2. A Note About Virtual Consoles (Red Hat)

Do you have xterm installed?

xterm is the standard terminal emulator for the X Window System.

Install it with:

pacman -S xterm