Corporate pilot reported an NMAC during pattern entry at a non-towered airport with another aircraft that was flying a non-standard traffic pattern.

Narrative

I was flying the aircraft and was returning to ZZZ and made the call to enter left base for Rwy XX. I was coming from NE ZZZ to enter a long left base to Rwy XX. There was chatter by the passengers in my aircraft and I mentioned to them about Sterile cockpit especially near the airport during landing and takeoff. As I was approaching I have been announcing my position from a distance. Again; I announced my left base call to full stop. I looked at traffic all along and I couldn't find anything visually. I announced my call on final (~ 1 mile) for a full-stop landing and heard one pilot saying he is moving away. I don't know where he was located at that time (approximately XA:20pm). Rwy XX has a left traffic pattern and I was on left base. I was told by my corporate organization people that the other pilot was coming on a right base to XX. Since he was moving away; I continued and landed since he was moving away. If the pilot made his call; I didn't hear it may be due to my passengers talking. However; I made the call and he should have heard it (left base call and final call). After this I flew back from ZZZ to ZZZ1 on another aircraft as a passenger. At around XB:00 pm; I heard from my corporate personnel (still at ZZZ after winding down the flying event) that the pilot of the other aircraft complained to them and my corporate people called me as per their process. Both aircraft were almost parallel on final for Rwy XX is what I was told (I didn't see that airplane at all and I was watching for visual traffic from all sides). I had my beacon; strobes; and landing light ON.Other corporate pilot flying the passengers in other airplane noted that the same pilot was landing (touch and go's) in the non-standard right traffic for Rwy XX at ZZZ for sometime and it is evident in flightaware.com. They said it is 'troubling' to manage the traffic with him.The aircraft that I was flying didn't have traffic display/alert capability. I find that the traffic display capability is a HUGE item in maintaining safety at uncontrolled airports. Also; non-standard pattern usage is a threat at uncontrolled airports.I'm thankful that nothing happened; but these situations can definitely be avoided.