I am afraid not.
But you may make your own game, using a different stroke colour for tracing, such as black/red or red/black (Smart Guides are your friends (at least for part of the game), saying anchor when you are close enough to snapt to an Anchor Point, and handle for Handles):
1) Create a circle with the Ellipse Tool, then ClickDrag horizontally (either way) from the top Anchor Point, then ClickDrag vertically down from the Anchor Point, then horizontally the other way, then vertically up, then horizontally at the top; you may adjust the Handles afterwards. You can see what they must look
2) Create an ellipse the same way.
3) Choose some raster images, starting with very simple ones, and trace their boundaries in a few goes in the same way as in 1) and 2), ClickDragging from different spots that may seem relevant; try reducing the number of Anchor Points each go.
4) Create some paths with the Pencil Tool and do as in 3), ignoring the Anchor Points apart from the first (and last) one.
5) Try to create shapes that you imagine.
A good learning exercise is to trace type.
Turn off all snaps (Snap to Grid, Snap to Points, SmartGuides).
Set some large type, using a quality normal sans-serif typeface which contains Type 1 outlines, not True Type outlines. (Because Type 1 outlines are drawn using cubic Bezier curves, whereas TrueType outlines are stored as quadratic Beziers. Type 1 outlines have fewer anchors and better represent the way you would efficiently draw paths in a drawing program.)
Give the text a light colored fill. Move it to its own Layer and lock the Layer, Draw on a separate front Layer.
Start with simple straight glyphs (E, A, T, F). Then use characters with bowls (B, P, R) to introduce smoothPoints. Then work on round glyphs (c, e, f, g, o) to involve curves which involve only smoothPoints and/or bothmoothPoints and cornerPoints which must work together. Then work on charcters which require ess curves (a, S).
As you proceed, always try to achieve each shape with the fewest anchorPoints, and by figuring out the fewest moves by using the momentary keyboard shortcuts (alt, shift, altShift).
Occasionally convert the text object you are tracing to outlines and compare how you drew it to how it was drawn in the font.
Work toward drawing the paths with good accuracy at the first go, without having to go back to tediously adjust curve handles. (But be sure to practice the keyboard shortcuts for doing that, too.)
When you've achieved reasonable accuracy then turn on SmartGuides and start learning how to use it to ensure horizontal / vertical alignment between anchorPoint placements as you draw, including alignment between the new anchorPoint and two existing anchors at the same time.
I think I am getting close to what I am looking for https://play.google.com/store/apps/details?id=cerb.bezierdrawing
Unlikely, I will ever practice on my home machine for very long when the wonderful safe familiar world of Photoshop is only a click away. I need a pen tool app. I can use on a phone/tablet to practice on during the odd down time moments at work (cannot down load anything to my desk work machine). A Bezier tool game would be the optimum, points for less points as Iwork my way around a maze or trace a picture until I nail the hand/eye/trajectory thing.
Oh well, with all the improvements that are being made to the pencil tool the pen tool might not be so critical in the future.
I know I will never get anywhere in Illustrator unless...
You follow that up with this?:
Oh well, ...the pen tool might not be so critical in the future.
And you're willing to count on that?
Sorry, but it sounds to me like you're just giving up before even getting started.
You don't need a video game to learn to use a drawing program's primary Bezier tool. You already have the correct environment in which to practice; the program you're using.
The user interfaces for the primary Bezier tools in all mainstream drawing programs differ in the details. Proficiency and speed depend upon those subtle differences. It's not like Mario Teaches Typing. There are differences even between the Bezier tools of Illustrator, InDesign, and Photoshop.