Why there is no article before venture capital firm in "Beller’s first high-profile role was at venture capital firm Andreessen Horwitz, .."?

Beller’s first high-profile role was at venture capital firm Andreessen Horwitz, where she was a partner on the deal team between 2013 and 2016. Source

Does the same rule apply to the sentence above as to the expressions like at work, in hospital, and at school? Is Beller’s first high-profile role was at a venture capital firm Andreessen Horwitz, where she was a partner on the deal team between 2013 and 2016. a correct variant as well?

Think of the sentence first as

Beller’s first high-profile role was at Andreessen Horwitz.

Now explain what the name means:

Beller’s first high-profile role was at venture capital firm Andreessen Horwitz.

You would not add an "a" in the first sentence, nor in the second, because the three added words are adjectival. Adding "a" would be an article for "Andreessen Horwitz", not for "firm".

But you can rephrase the sentence in two ways, where the punctuation separates the sentence into two noun phrases:

Beller’s first high-profile role was at a venture capital firm, Andreessen Horwitz.

Beller’s first high-profile role was at Andreessen Horwitz, a venture capital firm.

Now, the article "a" does indeed belong with "firm".