Interpreting cross-partial derivatives

Consider a duopoly setting. Firm $1$ has the following profit equation:
$pi_1(q_1,q_2,v_1)=(a+v_1-q_1-gamma q_2)q_1 .$
Where $a>0$ is a utility parameter, $q_igeq0$ is the quantity and $v_igeq0$ is the quality the of firm $iin1,2$, and $gammain(1,0)$ is the degree of product differentiation.(assume no cost – irrelevant).

Now, I first want to find the change in $pi_1$ when firm $2$ increases its quantity. Then I calculate
$frac{partialpi_1}{partial q_2}=-gamma q_1<0$.
Obviously, this means that $pi_1$ decreases when $q_2$ increases.

Arriving to my question:

I want to find the change in $frac{partialpi_1}{partial q_2}$ when $gamma$ increases. So I take the cross-partial derivative,
$frac{partial^2pi_1}{partial q_2partialgamma}=-q_1<0$.

How do I interpret this result?
Does this mean that "lower differentiation (higher $gamma$) weakens the effect of a larger quantity of firm 2 (higher $q_2$) on the profits of firm 1 ($pi_1$)?"

This makes no sense to me because just by looking at the profit equation above I can see that higher $gamma$ means a stronger effect of $q_2$ on $pi_1$.

P.S.
Is there a problem with taking the partial derivative w.r.t $gamma$ when $gamma$ is in an open set?

Thank you.