If we use Communication Services Package Sample App to make a video call, the receiver will always get the button "Accept Audio Call". So apparently the Communication Services Package Sample App does not know that the incoming call is actually a video call. Is there a way to know that an incoming call is a video call?

A call has a getIncomingVideoOffered() method, which has the description: "Determines if the incoming call includes video.". However the possible values it can return are 'INDEFINITE', 'OFF' or 'SUPPORTED', but no matter if we do a audio call or a video call, this always returns 'INDEFINITE'

Yes,

call.getIncomingVideoOffered() === AvayaClientServices.Services.Call.VideoNetworkSignalingType.SUPPORTED

should be the indication that the call is a video call. If that is not returning SUPPORTED I'd guess that the call is being received as an audio only call. Assuming the far end initiated a video call, then it is possible that the network is removing video from the call. A common gotcha is that the AAMS by default is not configured for video. I would check that the AAMS being used for the call is configured to allow video.