The score compares the sum of squared residuals (SSE) of your line to the smallest possible SSE, from the true least-squares regression line. A score of 100 means you found the optimal line exactly; lower scores mean your line leaves more total squared error than the best possible fit.
Why squared residuals instead of just the distance?+−
Squaring does two things: it makes every residual positive (so points above and below the line don't cancel out), and it penalizes large misses much more than small ones. A line that's close to most points but very far from one or two will have a worse score than a line that's moderately off from every point — that's by design, not a bug.
Why not just eyeball a line that looks balanced?+−
Eyeballing is exactly what this game tests — and it's harder than it looks, especially with noisy data. The least-squares line isn't always the one that looks most centred; it's specifically the one minimizing total squared error, which can look slightly different from an intuitive "balanced" line, particularly with outliers pulling it around.
Does a higher slope always mean a better fit?+−
No — the slope just needs to match the underlying trend in the data, whatever that trend is. A steep slope fits data with a steep underlying relationship; a shallow or even negative slope might be the best fit for different data. There's no universally "better" slope, only the one that minimizes squared error for this particular scatter.