Hebrew has a plural of excellence or majesty for nouns, but not a royal we for pronouns. Some people are confused about this because the terms are not kept separated correctly.
Based on what you write, Walter Martin writes about the royal we, which Biblical Hebrew does not have. However, אֱלֹהִים 'ělōhim (non-Israelite gods or the Israelite God) is a plural of excellence, which Biblical Hebrew does have.
Majestic plural / royal we
Narrowly speaking the majestic plural or royal we is the use of a plural pronoun to refer to a singular monarch, as in (for the reference see the Wikipedia page):
By the Grace of God, We, Alexander I, Emperor and Autocrat of All the Russias ...
As far as I know, when a pronoun is used to refer to God, a singular form is used. (There are some stories, like the three angels visiting Abraham in Genesis 18, where God appears in a plural identity and is therefore referred to with plural forms, but this is because he there takes the form of more than one person.)
The royal we is related to the T-V distinction in languages like French, which can use the second person plural pronoun (vous) as a polite / honorific form to address singular persons, instead of the singular form (tu). Biblical Hebrew has a different system for polite address; it avoids the second person and uses the third person instead. For example (1 Samuel 26:19):
וְעַתָּ֗ה יִֽשְׁמַֽע־נָא֙ אֲדֹנִ֣י הַמֶּ֔לֶךְ אֵ֖ת דִּבְרֵ֣י עַבְדֹּ֑ו
and now, let listen my lord the king to the words of his servant
And now, my lord the king, please listen to my, your servant's, words.
Joüon & Muraoka (2006: A Grammar of Biblical Hebrew. Rome: Gregorian & Biblical Press) state plainly (§114eN):
The we of majesty does not exist in Hebrew.
Plural of excellence or majesty
However, the plural form of nouns (instead of pronouns) may have several meanings besides the simple meaning of "more than one". Joüon & Muraoka list a great number of nuances of the plural (§136):
- Plural of extension: שָׁמַ֫יִם šāmayim (sky, heavens), because the heavens are composed of multiple parts
- Plural of composition: דָּמִים dāmim (bloods > bloodshed)
- Plural of intensity: בְּהֵמוֹת Bəhēmōṯ, for its greatness
- Plural of abstraction: בַּטֻּחוֹת baṭṭuḥōṯ (security, from sure circumstances)
(The word מַ֫יִם mayim (water) which you mention can be explained as a plural of extension or composition.)
There is also the plural of excellence or majesty, which occurs in words like:
- אֱלֹהִים 'ělōhim (non-Israelite gods or the Israelite God)
- קְדֹשִים qəḏōšim (the Holy One: Proverbs 9:10; 30:3)
- אֲדֹנִים 'ǎḏōnim (ordinarily lords or the Lord, especially in 'ǎḏōnāy my Lord)
It seems that this is, at least in poetry, not restricted to the deity: שֹׁלְחָיו šōləḥāw (he who has sent him: Proverbs 10:26); מְרִימָיו mərīmāw (he who lifts it: Isaiah 10:15).