The fact I want to know is whether I can use 'all over the world' with singular countable noun [sic].
Yes, you can.
A mum's love note to her baby has been reproduced by nearly 100 strangers - all over the world.
The handwritten message from Aimee Crook, 20, to her son Leo has already appeared in multiple countries - including America, Canada, Mexico, Australia, Egypt and France.
However, in the OP's sample sentence,
There is no place all over the world where football is not played the term "football" is used as an example of a singular countable noun. The sport called football is uncountable, while the round (soccer) or oval ball (American football) is countable.
- My mom buys me footballs from all over the world. (plural countable noun)
I have a football that has traveled all over the world. (singular uncountable noun)
Another example of usage, taken from the BBC website
The rainbow flag is a symbol for gay pride all over the world.
This can be changed to
- All over the world, the rainbow flag is the symbol of gay pride.
- The rainbow flag all over the world is the symbol of gay pride.
- The rainbow flag all over the world symbolizes gay pride.
TRomano's answer addresses the grammaticality of the OP's sample sentence very well, so there's no point in my repeating it.