He has a soft spot for playing hard ball
Not really a pun, I think. What is the exact term?
And correct me if the title can be made better.
This is a rhetorical device known as antiphrasis.
An example of this would be Perdue Chicken's advertising tag line of a couple decades ago:
Note that the irony is established by context, i.e., reference to another part of the sentence or to an obvious fact. In the examples above, note that "Tiny" and "cool" are used in deliberate contrast to information related later. This differs from simple irony, which is a statement whose intended meaning is the opposite of its literal one, in that it must play on that opposite within the statement. For example, in the "Tiny" example, if the speaker were simply to say to the fat man
That would be an ironic statement but it would not be antiphrasis. Antiphrasis requires the play of "tiny" and "fat" for its effect.
I would just carry on calling it juxtaposition...
"Juxtaposition is a poetic and rhetorical device in which normally unassociated ideas, words, or phrases are placed next to one another, creating an effect of surprise and wit: The apparition of these faces in the crowd:/Petals on a wet, black bought (“In a Station of the Metro” by Ezra Pound)."
"JUXTAPOSITION: The arrangement of two or more ideas, characters, actions, settings, phrases, or words side-by-side or in similar narrative moments for the purpose of comparison, contrast, rhetorical effect, suspense, or character development."
(Latin for 'to join' and 'to place') is a placing in nearness or contiguity, or side by side, often done in order to compare and contrast the two in order to show similarity and differences. Usually Creates an effect of surprise and wit. Juxtaposition is also a form of contrast by which writers call attention to dissimilar ideas or images or metaphors.
An example could be Martin Luther King's letter from Birmingham Jail: “Injustice anywhere is a threat to justice everywhere.”
The first (main) clause has to be idiomatic. 'He' is not talking about a medical condition. To play hard ball can also be used idiomatically, and often is (to 'take a hard line'), and we'd then have a mixed metaphor (which devices are often used humorously) if that were the case here. However, the meaning does not sensibly allow for a non-literal meaning of 'playing hard ball' here:
??He has a soft spot for taking a hard line.
When he's not sleeping furiously!?
Surely a contradiction in terms rather than an oxymoron.
I've once been in a discussion about whether the term 'mixed metaphor' is/should be applied to cases where there is only one metaphor but its use jars - whether humorously, as here, or ludicrously or otherwise inappropriately - with the rest of the sentence. We decided that the term inappropriate metaphor was more accurate if less mellifluous.
Whatever the actual construction should be called, your example is certainly a play on words (probably even if unintentional), and, since it relies on different polysemes (hard the principal physical sense but soft the derived emotional sense), I think many people would allow it into the class of puns.