The correct option is
B playing
The verbs that do not explain the tense of the sentence and do not agree with the subject are called non-finite verbs. Non-finite verbs are usually infinitives, gerunds and participles.
Option A - 'Play' is the original form (present tense) of the verb. However, 'play' is a finite verb. As explained above, non-finite verbs are usually infinitives, gerunds and participles, we can't use 'play' here. Hence, option A is incorrect.
Option C - 'To be playing' can be used in passive voice. As the sentence is in the active voice, we can't use 'to be playing' here. Also, it is grammatically incorrect to use. Hence, option C is incorrect.
Option D - 'Have been playing' is the present perfect continuous tense of the verb 'play'. It is a finite verb here. Also, as the sentence is in simple present tense, we can't use 'have been playing'. Hence, option D is incorrect.
Option B - 'Playing' is the participle form of the verb and is a non-finite verb here, as it doesn't explain the tense of the sentence. Hence, option B is the correct answer.
'My favourite pastime is playing video games.'