Where does “blockhouse” come from?

I need to work through this etymology chain carefully, but I notice there's a significant problem: the chain provided doesn't actually form a coherent path to "blockhouse." The chain lists: English house → Middle English hus → Middle English -en → Middle Dutch blok → Old Dutch blok → Proto-Indo-European éǵh₂ → Proto-Indo-European bhulg'- → Proto-Indo-European bhelg'- This chain seems to conflate two different etymologies: 1. "house" (from hus, éǵh₂, etc.) 2. "block" (from blok, bhulg'-, bhelg'-, etc.) But the headword is "blockhouse," which would be a compound of both elements. The chain as presented doesn't show how these two elements combine or how they both contribute to the modern word. Additionally, I'm asked not

blockhouse (English): A sturdy military fortification, often of...

Definitions

  1. A sturdy military fortification, often of...

Ancestry of “blockhouse”, step by step

blockhouse traces back through two separate lines of ancestry.

via English block

StepLanguageWordMeaning
1EnglishblockA substantial, often approximately cuboid, piece...
2FrenchBlocBloc — Bloc Québécois (Bloc québécois)
3Middle Frenchbloca considerable piece of something heavy, block
4Old Frenchbloclog, block
5Dutchbloka block; a street block; a political bloc
6Middle Dutchbloktreetrunk
7Old Dutchbloklog
8Proto-West Germanicblokkblock, log
9Proto-Germanicblukkąblock, log
10Proto-Indo-Europeanbhulg'-
11Proto-Indo-Europeanbhelg'-thick plank, beam, pile, prop

via English House

StepLanguageWordMeaning
1EnglishHouseA particular chamber of political representation
2Middle Englishhoushouse, residence; house of worship, temple;...
3Old Englishhūsdwelling, shelter, house; house
Every word from Proto-Indo-European bhelg'-