The short answer is that no, they do not mean the same thing.
The first with an inflection of the progressive construction be playing is a simple statement of the evidentiary future, but the second with an inflection of will play is a statement of a future that the speaker insists must come to pass.
Probabilities vs Demands
When someone says:
I will not ...
This is reported speech, where we backshift tenses. Backshifting happens when a verb tense is shifted back to a past form in reported speech.
What was said by John: "I am hungry." In reported speech, we see "John said that he was hungry."
In your example "I told him I wasn’t playing soccer anymore", what was actually said was &...
One can write a sentence with a partial quotation:
Direct speech: We live in a madhouse! We have to move.
She says they "live in a madhouse" most of the time.
This is unobtrusive: the quotation is direct speech, because the exact words are repeated, made to fit into the syntax of the sentence, which was easy enough. It is a predicate, so it fits ...
Be is not always required to mark passive voice. There are other constructions like the one in the example given where the passive is not marked by be (CaGEL p1245):
i Most of the sense verbs
I heard the window broken.
ii Get and have:
She got/had the house painted.
I had my wallet stolen.
iii Like, want, report,fear and order; here the past-participial is ...
If looking only at the phrase itself without any context, the report finished is an active-voice construction.
Semantically, it's strange. It's ascribing an action to a report—something that isn't normally done. But that doesn't make it any less an active-voice construction.
The following sentences are in the active voice:
The dog jumped.
The woman laughed.
There's no "exact" way to convert exclamatory utterances from direct to reported speech. Here are my best efforts for a few typical examples...
1: "What a pity!" said John = John said it was such a pity
2: "How kind of her!" said John = John said she was very kind
3: "Thank you, Jane" said John = John thanked Jane
Well, one of the ways you can use the word "want" (as well as the phrase "would like") is by putting a noun and a passive participle after it. Examples are:
I want this building demolished. (The meaning is similar to "I would be happy if somebody demolished this building".)
I want him out. (The meaning is similar to "I ...
(1) I agree that the sentence you mark as wrong is much better without the that; (2) do not look to Wikipedia for good English. I would leave the that out in both sentences, the one you marked wrong and the one you quote from Wikipedia.
'Would + verb' either stays the same (if it is a more general statement), or can, but does not need to, change into 'would have + past participle' (if we are hypothesising).
'I would buy it if I had the money,’ he said. -> He said he would buy it if he had the money.
‘I’ll help you if you need a volunteer’ / ‘I’d help you if you needed a volunteer.’ -> He ...