I would like to play this game. Watch the commercial here. In 1977, Ideal repackaged it as Battling Spaceships for obvious reasons. A game board was added around the fighting ring, but the battling part is exactly the same. The box and commercial are below.
See more at Board Game Geek.
2 Warps to Neptune 
Hi 😀 Love, #WOW “BattlelingTops” ,I have not played that game in 40 years. I never played “BattlelingShips” I play “Battleships” “Bonic Women” “Bonic Crisis” “Six Million Dollar Man”
I wonder if they have an up dated version “Battleling Tops” Amazing what the past parlor games are not forgotten
Sincerely,
Kula May 😀
They do have an updated version of Battling Tops but it is HORRIBLE! So cheaply made. You use a rip cord that fits into grooves on your top and the plastic is so cheap that after a few pulls the grooves break off. I work with children and they hated it but loved my original Battling Spaceships which still works some 35 years later!!
Battling Spaceships sucked because of the stickers in the arena. Those tops would hit them and would spin them out of control. It would have been better to have left them out. What’s a nine year old suppose to do!