Simple undirected graph. A graph is simple if there is no self-loops and multiple edges, and undirected if the edges are undirected.
Hasse diagram. In a Hasse diagram, the edges $u\rightarrow v$ are drawn in the plane such the vertex $u$ is placed below the vertex $v$ and there is an undirected edge $u-v$. By doing so, we can drop the direction in a Hasse diagram.
Can we treat a Hasse diagram as a simple undirected graph in graph theory or computer science?
The most general answer would be "it depends". Hasse diagrams do have vertices and edges, so technically they may be seen as graphs. However, if we wish to analyze the relations through these graphs, this could pose some problems. Firstly, if we had edges $u-v$ and $v-w$ in the Hasse diagram of a relation $\sim$, this means that due to transitivity of the relation we have $u \sim w$ - however, this relationship is not explicitly depicted in the Hasse diagram. Secondly, if we treat the Hasse diagram as an undirected graph, we lose the information resulting from the orientation of the Hasse diagram - it happens because graphs do not have orientation. If we flipped it upside down, it would not change the graph. However, we cannot flip the Hasse diagram upside down, as we would get a Hasse diagram of a completely different relation.