Yes, an integer literal is an object in Python. To summarize, the parser needs to be able to understand it is dealing with an object of type integer, while the statement 1.real confuses the parser into thinking it has a float 1. followed by the word real, and therefore raises a syntax error.
To test this you can also try
>> (1).real
1
as well as,
>> 1.0.real
1.0
so in the case of 1.real python is interpreting the . as a decimal point.
Edit
BasicWolf puts it nicely too - 1. is being interpreted as the floating point representation of 1, so 1.real is equivalent to writing (1.)real - so with no attribute access operator i.e. period /full stop. Hence the syntax error.
Further edit
As mgilson alludes to in his/her comment: the parser can handle access to int's attributes and methods, but only as long the statement makes it clear that it is being given an int and not a float.