The answer of your question -
Is Kalki Avatara a murderer of Buddhists is No according to Shreemad Bhagvat Purana. Skandha 2 Chapter 7 : SB 2.7 : Scheduled Incarnations with Specific Functions and Skandha 12 chapter 2 : SB 12.2 : The Symptoms of Kali-yuga.
It says -:
यहर्यालयेष्वपि सतां न हरे: कथा: स्यु:
पाखण्डिनो द्विजजना वृषला
स्वाध्या स्वधा वषडिति स्म गिरो न यत्र
भविष्यति कलेर्भगवान युगांते ॥38॥
yarhy ālayeṣv api satāṁ na hareḥ kathāḥ syuḥ
svāhā svadhā vaṣaḍ iti sma giro na yatra
bhaviṣyati kaler bhagavān yugānte
Thereafter, at the end of Kali-yuga, when there exist no topics on the
subject of God, even at the residences of so-called saints and
respectable gentlemen of the three higher castes, and when the power
of government is transferred to the hands of ministers elected from
the lowborn śūdra class or those less than them, and when nothing is
known of the techniques of sacrifice, even by word, at that time the
Lord will appear as the supreme chastiser. SB 2.7.38
विचरन्नाशुना क्षोणयां हयेना प्रतिमद्यूति:।
vicarann āśunā kṣauṇyāṁ hayenāpratima-dyutiḥ
dasyūn koṭiśo nihaniṣyati
Godhead. Displaying His unequaled effulgence and riding with great
speed, He will kill by the millions those thieves who have dared dress
as kings. SB 12.2.20
Now if we look at the verse no.38 and verse 20 we can see the exact purpose ok Kalki-Avatara , In Kali-Yuga When there will no Katha-Kirtana will get performed even at the homes of most spiritual oriented people , Brahmana , Kshatriya's and Vaishya's will became atheist (nastika) ,Shudras will became kings ,and there will no sound heard of Swaha ,Swadha and Vashtkara ,at that time Lord will take Kalki avatara to punish Kali-Yuga and those thives who have falsely dressd as kings
The Kalki will punish Kali-Yuga and demons and nor the buddhist people , it doesn't saying anything about murdering of Buddhists. Buddha is considered a Avatara of Lord Vishnu here.
we can see that the lord himself will assume dress of buddha and will preach false dharma , when Danavas by using knowledge of vedas and becoming invisible reciding in City of Maya Danava ,will cause destruction of the people.
So according to me the answer will be simply No.