Unknown kanji (to me) in a boxscore?

That is "furinige" or "swing and run."

And your interpretation is correct. It's when a batter swings and misses a third strike, the catcher fails to catch the ball properly, and the batter takes first base.

When I saw the subject line, I was sure you were going to ask about 打妨 (as happened in the Yokohama vs. Hanshin game on April 14. My first impression for that one was "batter's interference" since the kanji are literally "hit" and "interfere." However, I saw this one, and it was the batter that was interfered with - catcher's interference by Yano. Since this scoring is looking at it from the perspective of who is interfered with instead of who does the interfering, it explains why 野妨 would be an out - because the fielder was interfered with.

The big question I have is, how does one score these? 打妨 will most likely always be "catcher's interference." However, would 野妨 always be "runner's interference"?

Well, I can tell you that I'm translating that as "KA", or "strikeout but runner advanced." The second kanji means "escape," doesn't it?

Escape is one meaning, as in the old TV series (made into at least one movie) "The Fugitive" - 逃亡者. It was also used heavily in the news when Orix's Maeda committed a hit-and-run [Nikkan Sports - in Japanese] this past off season.

Space Alc is a great resource for exploring the meanings of various kanji combinations. (Unfortunately, their baseball-specific vocabulary isn't very strong.)

It is Dageki bougai (打撃　妨害) - catcher's interference.
Shubi bougai (守備　妨害) is offensive interference.
Sourui bougai (走塁　妨害) is obstruction.
Yashusentaku (yasen) (野手選択) is Fielder's choice.

Thanks. Those are much better than my definitions.