Hey all, posted a similar game a few months ago for memorizing the notes of the fretboard. This time round it's intervals/interval functions/scale degrees .
This game is just for the ascending scale degrees and comes with an accompanying course to learn them (https://www.fretboardfly.com/learn/FBG-201). There are similarly other games for descending scale degrees and its accompanying course (https://www.fretboardfly.com/play) and (https://www.fretboardfly.com/learn)
Then you can just use solmization in your mind to figure out how to build any scale pattern on the fretboard regardless of key, keeping in mind that e.g. ut-fa is always a perfect fourth, ut-mi a major third etc. and that mi-fa is always the semitone interval. (There is no ti in historical solmization, you just sing sol-re-mi-fa for the upper tetrachord then pick up again with re-mi-fa etc.) Memorization comes most easily from repetition, the deliberate effort should go towards figuring out the underlying patterns and how to think of them most intuitively and musically.
(BTW, solmization is also very helpful in making musical sense of isomorphic keyboards, which much like the guitar fretboard are essentially non-diatonic. It helps you keep track of where the semitone intervals are in a musical line, since they will always be associated with mi and fa.)