Prison Architect is perfectly playable without a keyboard, but you might be hampered by missing a mouse wheel for clicking and scrolling.
Looking at this list of controls:
- WASD to pan the camera. This can be done by middle-clicking and dragging, or moving the mouse to the edges of the screen. If your pen must issue a left click to move the cursor (as opposed to moving it without clicking), you can still left-click and drag to the edges of the screen, you'll just end up selecting a bunch of stuff as you pan.
- QE to zoom. This can be done by scrolling the mouse wheel, so if you don't have one you'll have to bring up the keyboard to zoom. You can play just fine by getting a good zoom level and sticking with that, and only zooming out rarely to view your entire prison for mental planning (I do this even with a mouse wheel, there's a zoom level I like and anything else looks too blown up or too small).
- R to rotate object. This can be done by clicking the mouse wheel. If you can't middle-click, this is going to be a problem. Rotating square objects is only decorative, as the direction doesn't make any in-game difference. However, rotating rectangular objects is important so you can place the object vertically or horizontally.
- Space / 123 for pausing and time speed control. There are buttons in the UI for this.
- H to direct the fireman's hose. Firemen will put out any fires near them, but you can tell them where to point using H. Not really necessary.
If your pen has a third button, you can map it to middle-click with AutoHotkey and play with only the zoom / fireman's hose not available (you can't remap right-click since that's used to cancel jobs, which is important).