Cleve Moler was one of the big names in numerical methods, and participated in creation of canonical FORTRAN libraries for solving linear equations, and matrix algorithms more generally. To teach this more conveniently to his students, he wrote the original version of MATrixLABoratory to allow interactive exploration of the library functions without having to compile FORTRAN code. The original version was about 2000…
Fun anecdote about early Matlab. In the '80s, while in high school, I "acquired" the source code of an early version of matlab, similar to the one that you linked. An email from Cleve Moler in 1990 asked people not to distribute the code, so I didn't give it to anybody. In the late '90s I visited Cleve Moler at his Mathworks office, and he proudly showed the early Matlab running on DOS, remarking that he only had that binary but had lost the source code. So I gave it to him.