The passage can be made to mean what the author wants it to mean, although the meaning produced is absurd. "For whatever reason," the author shrugs, two men who lay down in a bed that belonged to a woman should be put to death. Whatever reason, indeed! As this person correctly notes at the bottom, men were forbidden from "lying in the bed" of a woman at certain times; in other words, while she was menstruating. Curiously, Leviticus 20:21 doesn't mandate the death penalty for lying in a menstruant's bed, but Leviticus 20:13 somehow mandates the death penalty if another man is with him when he does?
A far simpler and considerably more logical explanation (however repugnant the author of that piece may or may not find it) is that the word mishkav (which is not a noun, but a participle) denotes not only a "bed", but also "the act of lying down" - a bivalency of meaning common to all Biblical Hebrew participles - and "the act of lying down" is a euphemism for coitus. In that case, משכבי אשה (mishkevei isha) does not mean "the beds of a woman", but "the lying-down of a woman" - ie: a female way of having sex.
Truth be told, this word has long posed problems for Hebrew grammarians, and not only in this form. One of the ways in which Hebrew refers to semen is שכבת זרע (shikhvat zera') - eg: Leviticus 15:16. If you wanted to be an extreme literalist, you could translate this as "the lying down of seed", only that's clearly not what it means.
Ultimately, if this is what you want the Hebrew passage to mean, you can make the words mean that, however incongruous or absurd that might make the passage, and however bereft of historical precedent such a reading is. The fact that nobody has ever suggested this in the past is not because "the Jewish people consider the text of the Hebrew Bible so sacred, that they will not alter even simple grammatical errors", but because it takes a special type of arrogance to think that untold generations of people failed to recognise a simple grammatical error that you, yourself, can see.
The study of Hebrew grammar is a way of making sense of the biblical text; not a scientific endeavour to which we can then subject the Hebrew Bible as a way of spotting mistakes that its authors made. And while I'm criticising the historical presuppositions:
- There is ample evidence of dialectal variation long before the mediaevals (indeed, even within biblical, extra-biblical and early post-biblical texts);
- Ancient Hebrew originally featured what's known as an epicene pronoun (for which reason הוא can sometimes represent what is usually conveyed by היא);
- The scholars who produced the Masoretic Text made numerous emendations to it, both in the realm of lexis and of grammar;
- The scholars who translated the text into Aramaic (the Targums), into Greek (the Septuagint), into Syriac (the Peshitta) and into Latin (the Vulgate) didn't find this passage confusing, and rendered it as a prohibition of same-sex intercourse;
- The scholars who have studied the text closely over the last two millennia haven't all been Jews.
Also, although you can take this with a grain of salt, there is no reason to suppose that the Pentateuch was composed by a single person, and even if you were to suppose this (and were to suggest that he didn't understand Hebrew as well as the author of that website does), then you need to reckon with the fact that these same "mistakes" are made in subsequent texts of the Hebrew Bible as well. That sounds like a pretty tall order to me.