Chain Puzzle: Tabletop Games #06 - So Sorry

_{This is the sixth Chain Puzzle in the Tabletop Games series, in which all puzzles are themed around board games, card games, tile games, and the like. The answer to this puzzle is a thematic word or phrase. The solver whose answer is awarded the green checkmark has first refusal on the opportunity to create the next puzzle in the series, which must somehow incorporate the answer to this puzzle somewhere within its construction. The solver is under no obligation to create the next puzzle – in the event that the solver does not wish to take up this opportunity, the puzzle’s setter may take up the offer of a willing substitute setter or choose to continue the chain themselves.}

_{The answer to the previous puzzle (which provided the theme for this one) was SORRY.}

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I’m so sorry to not come up with a story
so let me apologize with this piece of poetry.

This time you’ll solve a Hitori
but not one of the ordinary,
as the black cells will have a buddy,
otherwise they’ll be so lonely…

Once you’ve solved the Hitori,
read the rows using the rules of Sorry,
and you’ll see the next game to play.
Beware, every single rule counts!

Solve the following Hitori Blocks puzzle, and apply Sorry rules to identify the four-letter name of the next game. It’s up to you to find out how to apply the rules on the completed grid.

Rules of Hitori Blocks:

1. (Hitori rule) Shade some cells black. Shading a cell erases the number in that cell.
2. (Hitori rule) Unshaded cells must be connected, and no row or column may have more than one occurrence of any given number.
3. (Variant rule) Shaded cells must form dominoes. No two dominoes may share an edge.

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The hints are crossposted to the Chain Puzzle chat room. Note that the chatroom may contain other spoilers.

Hint 0-1:

Hint 0-2:

Hint 1:

Hint 2: (revised)

Hint 3: (read as Nobody’s getting visible progress, so I’d just drop the intended interpretation of the Hitori solution in order to prevent the chain from dying. Sorry!)

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_{Chain Puzzles are a novel approach to puzzle series creation, in which the solver of the previous puzzle in the chain becomes the setter of the next.}