Linguistic gender has nothing to do with real-life gender. It is just a categorization for words. Arabic has no neuter gender (like German or Russian for example) but only two genders: Masculine and Feminine (more like Spanish, French, Italian etc).
On the other hand, there are languages that do not have the concept of gender, like Turkish and Persian.
According to my own research, I think the Arabic word is indeed borrowed from Latin. Moroccan in fact say (Táblah) instead of (Táwla) or (Táwilah) and probably they are influenced in this by Spanish. However, the word طاولة now is accepted as a normal Arabic word.
This said, however, there is indeed a word for "table" in Arabic though not used a lot in literature as far as I remember. This word is منضدة (minDHadah), and the word is derived from a verb about "organizing objects" or "set up" objects.
Tables might vary in the Arabic culture but surely they were used in one way or another, for food or other commodities. And this is not something specific to the Arab world alone in fact; It was something common for all cultures in the Middle East and even Far East.
On a side note, there are also two words related to table:
- xiwán خِوان: Also a table, probably more linked to low level table.
- má'idah مائدة: It is also a table or "xiwán" but when food is served on it. If the table has no food on it then it is "xiwán" only.
The second word here is also used sometimes for "table" regardless of its original meaning in classical Arabic.