Question!

(3) and (4) have effectively the same meaning, but there's small grammatical and technical differences which may or may not be forgotten by most people.

No, 3 and 4 are not completely the same.
The correct way to say it is (3).
I like to play baseball (野球をするのがすきです）

Explanation.

Difference between simple present/past("to play") and continuous present/past("playing") tense:

-CONTINUOUS is used when one is refering to what is taking place now. It also describe an action that takes place in a certain time span, which is taking place at a implicit time (now, then). The verb (動詞は大切です） is important.
(eg. My dog is dying now)

- SIMPLE is used with repeated actions or about something that happens all the time:
(eg: the sun sets in the west all the time.)．or when you are declaring something and you are not focusing on the verb. (eg: my dog died.)

In your example about liking baseball, it will in almost all cases be "I like to play baseball" because it is something that is not limited by a certain amount of time.
I like playing baseball isnt really a right usage but I suppose you can say "I like playing baseball in uni." （例：大学のころ、野球をするのが好きです）where it is defined by a period during uni and the action was ongoing then.　（大学生の時、好きなので野球をしていた　の意味）

I actually agree with Felathenin that there are grammatical and technical differences between the two sentences but the meaning remains essentially the same.

In "I like playing baseball." 'playing baseball' is the object of the verb. A time frame isn't necessary.

They are both correct and have the same meaning. 1 and 2 are both odd - 'on' rather than 'in that ground' - 'in that ground' sounds like they are talking about the kind of soil the baseball field is made of. "playing baseball" isn't a continuous tense at all in these examples - it's a gerund - a noun phrase - like 'skiing'.

There is a difference between "to play" and "playing" in general, but of the two example sentences given, the difference is minimal in speech, where people aren't going to kill you if you use a verb tense incorrectly.

If I had to be pedantic, (3) could be rewritten as "(Actually) Playing baseball is something I like" and (4) as "The act of playing baseball is something I like".

"Playing" here isn't a verb tense - it's a gerund - a noun.

Yes, I understand where you are coming from refering it to gerund, but where a verb is treated as a noun phrase. However, the way we were taught, only verbs that make sense can be treated with "I like", eg: I like boxing, I do not like skiing, where the verb itself is already understood. We like playing baseball" alone isnt the way we are taught, unless it is attached to place or time once u add a noun "baseball" to it. Then again, different countries have different teaching approach. It's whatever that make sense and understood. And yes, I know the meaning is essential the same but i just think it is important to share the technical differences. Cheers!