TeX was created before Open Source was formally defined. Its use is not restricted; it is stated explicitly in Knuth's writings that its methods and algorithms may be used freely for any purpose, whether personal or commercial.
The request that changes to the program under its original name be made only by the author is made for the purpose of maintaining user integrity and consistency, and avoiding confusion by having a manuscript prepared with a changed version submitted for publication to a journal that uses TeX in production. (A number of mathematical publishers do depend on TeX for their book and journal production. I retired from one such where the production stream has depended on TeX for more than 30 years. Dependability is a must in such an environment.) This requirement was considered sufficiently compelling that it was accepted into the Open Source Definition as noted by another answer.
Knuth still accepts bug reports on an announced schedule (see the "Errata" section at https://www-cs-faculty.stanford.edu/~knuth/abcde.html). This year (2020) is the review year designated in the present cycle, so if you have anything to report, please submit it by November; the next review won't occur until 2028.
The ur-TeX program has been expanded into a number of different variants, each with its own particular features, and all distinctly named, so that a user knows exactly what s/he is getting when selecting (or requiring) a particular variant, as does a publisher when receiving a manuscript. This saves considerable time and expense; preparing technical material for publication is complicated enough without having to deal with unannounced "improvements".
A statement by Knuth covering usage of TeX was included in his comments on the occasion of the "coming out party" for the five volumes of Computers and Typesetting, held in Boston on 21 May 1986, and published in TUGboat 7:2, 95-98 (https://tug.org/TUGboat/tb07-2/tb15knut.pdf).
The following quote appears near the bottom of page 97, column 1:
All of the methods described in these books are in the public domain; thus anybody can freely use any of the ideas. The only thing I'm retaining control of is the names, TeX and METAFONT: products that go by this name are obliged to conform to the standard. If any changes are made, I won't complain, as long as the changed systems are not called TeX or METAFONT.
Here's another, more recent, statement by Knuth regarding the status of TeX and the reason for the request that the name be restricted to his direct work: "The future of TeX and Metafont" (https://tug.org/TUGboat/tb11-4/tb30knut.pdf published in 1990).
