You have absolutely hit the nail on the head! The interface(s) to Spacewar are a bit confusing.
(Firstly, yes, if the VC8 app fails to connect etc., the terminal window will not be reset correctly ... Fixed as below).
In essence, there are 3!
I assume your VT220 is connected to the primary teletype channel to your PiDP8I (device code 03/04). This is the Spacewar option control channel.
On your (presumably) remote system running Linux there are 2 further windows ( a and b)
The a window is the one where you typed ./vc8_remote <host> where <host> is the name of your PiDP8i.
The b window is the SDL graphic display.
With your VT200, you can control only the options for Spacewar. Just type ucase O (Oh!) and the options will be listed. And, eg type 'F' for a field of stars etc.
The a window on the Linux system only responds to an lcase x which exits the app. This is so you don't inadvertently exit the app with a wrong key in the graphics window.
The b window is the one that controls the ships with 1,2,3,4 - 9,0,-,=.
With the original version of the Spacewar binary , the way this app works was to read the PiDP8I console switches to control the ships.
The current Spacewar binary is actually built with some additional code that allows the console switches to be 'set or cleared' by sending a 2 byte command code to a second teletype interface on device code 40/41 (a convention).
This interface is provided in Simh via the TTIX/TTOX device.
Using this, it is not possible to use the VT200 keyboard to send the command codes to control the ships.
These codes are only sent by the VC8 app from the SDL graphics window.
In fact, it is very difficult to get this remote interface to behave well via a standard terminal ie your VT200 or putty etc. The reason for this is that there is no keyup event.
So if you typed '2' (rotate) into the VT220 the ship would continue to rotate even after you released the key .... v annoying!
NB Update below also contains some slowdown code. The gives a better display on a standard PC.
I hope this helps!