I know that erasing G-d's name from a handwritten tanakh scroll, will render it non-kosher, but will accidently erasing G-d's name in a printed tanakh render it not fit for use? If so, does this apply even for non-Hebrew texts?
Mil, You may need to gain some sense on what items are considered "holy objects". I don't recall the full list, but among them are Torah scrolls, mezuzah, tefillin, etc. (I'll see if I can link something later).
The point is that a printed Tanac"h is not within this category of what is called tashmishei kedusha ("holy objetcs"). That doesn't mean that you can treat is as a novel and just dispose or deface it, intentionally. But, even if an entire page were ripped out, you can still use the rest of the book. There is no concept of "fit for use" or "kosher" use for printed books as there is for a Torah, mezuzah or tefillin, etc.
There are two related ideas - *holy objects" and "Mitzvah objects" discussed in Talmud Megillah. I cited this, below, so you gain some understanding of what these area. As you can see, a printed "Tanac"h" is not in either of these categories.
Megillah 26b:22-26 (Sefaria translation):
תשמישי מצוה נזרקין תשמישי קדושה נגנזין ואלו הן תשמישי מצוה סוכה לולב שופר ציצית ואלו הן תשמישי קדושה דלוסקמי ספרים תפילין ומזוזות ותיק של ס"ת ונרתיק של תפילין ורצועותיהן
Accessories used in a mitzvah [when worn out] may be thrown away; accessories of holiness are must be placed in a geniza. The following are accessories used in a mitzvah: A sukkah, a lulav, a shofar, tzitzit. The following are accessories of holiness: large sacks for scrolls of Scripture, tefillin and mezuzot, a mantle for a Sefer Torah, and a tefillin bag and tefillin straps.
This article described how to handle tashmishei kedusha, in general and briefly.