Two considerations I'm aware of:
Assuming this is based on overlaid inks (e.g. CMYK) not premixed inks (e.g. Pantone spot colours), it's not a bad idea to try to minimise the number of inks used in the colours in thin or high detail areas such as thin lines and fine text.
This is because for fine lines, tiny registration errors (different colour ink plates or layers being mis-aligned to each other by very small amounts) become noticeable, making a line that should be sharp look blurry or, in extreme cases, giving the appearance of separate adjacent cyan, magenta, yellow and/or black lines.
Here's an example of misregistration borrowed from a CreateSpace thread. What should be thin black lines in this type are slightly blurry with an unintended yellowy glow, from the yellow and magenta inks being printed slightly too far down and left.
So, for this pictured design, I'd normally set the diagnonal lines' strokes (and also the "A GAME BY DAVID SCOTT" thin text) to pure K "plain" black (0C,0M,0Y,100K), while keeping the solid blacks (border, shield, etc) as rich black.
Normally, you'd never allow two mixes of black to touch each other like how the 100%K diagonals touch the rich black border, because it would create a false edge between the two blacks - but in this case there's already an edge where the border stops.
If it was a design based on a different colour, I might try to find a variant of that colour for the thin details that was a close match but used the minimum number of different inks.
This is usually more important for text (preserving readability) than for decorative lines though.
DPI / LPI of the print setup
Not to be confused with the PPI of a digital file - this is about the capabilities of the print setup (including paper type). This is probably not an issue unless you're printing super-thin lines below 0.25pt, or printing to a low DPI/LPI setup, e.g. poor quality paper (e.g. newsprint) or large format (e.g. billboard).
Most printing involves your (presumably vector) image being converted into an arrangement of dots of C,M,Y,K ink. The print set up will have a maximum number of dots it can print per inch. If your line is thinner than one of the printer's dots, it's going to struggle to get close to looking like a perfectly crisp and straight line.
If the print specs mean this is likely to be an issue, find out the details from the printer and adjust the "0.25pt minimum" rule of thumb accordingly. For a box for a card game, however, this would almost certainly not be a problem for a 0.5pt line (unless it's a really ropey printer place).