I've only ever played regular pictionary ... but ...
the numeral "1" is absolutely a symbol. (I accepted immediate disqualification for foolishly using 666 to indicate evil
)
An arrow is, maybe, perhaps, just barely a symbol. I'll consider this in a moment, but as a matter of precedent if an arrow is a symbol then "1" certainly is.
In general, what is a symbol? Just pulling this out of my ear, but: a symbol is a drawn shape (or similar) which
by convention stands for, or represents, something else.
You're all welcome to pick over this definition.
But by this analysis, "1" is a symbol, because by convention it represents the amount one.
Is an arrow a symbol? does it by convention represent anything? I think yes, just barely. It represents an instruction, which may be paraphrased as "direct your attention to objects in the line indicated by the axis of this arrow, extended through the pointy end".
The key to this definition is the difference between representing by resemblance and representing by convention. Your sketch represents a face with a unibrow, because it resembles it. However it is not a symbol because the representation is based in resemblance.
The arrow represents an instruction, and it is a symbol because the representation is by agreed convention. I think this is right at the edge of what counts as a symbol, though. Imagine if you had simply circled the unibrow, or put a dozen little lines radiating out from it ... or simply drawn it extra heavily (as you did) ... it gets harder and harder to interpret these as convention-based symbols.
Maybe, and this is being rabbinically hair-splitting ... the arrow is a convention-based symbol
if it is some distance away from the thing it is pointing at. If it is touching (as yours is) it is more like underlining, drawing heavily, or circling.
Take home message: 1 is definitely a symbol. Arrows are maybe just barely symbols. Your friends are poor sports and poor philosophers.
My brain hurts.