Does distance of one user from WiFi AP have negative impact on other connected users?
Yes, this is true at least in the traditional 802.11 network.
Why? By the nature of 802.11 wireless, a channel (i.e. frequency range) is a shared medium. Only one device can be using the channel at a single moment in time. So a device connecting at a lower data rate will potentially consume more of the "airtime" available for communication; using more airtime to send/receive the same amount of data.
There are a couple of features in many modern 802.11 networks that mitigate or reduce this impact. Some wireless systems provide for client "airtime fairness" mechanisms. By manipulating the traffic in some fashion, each client is given an equal amount of time to use the channel, passing as much data as it can during it's allotted time.
Second, starting with 802.11ac, multi-user MIMO (aka MU-MIMO) was introduced. Combined with beam forming, this allows an 802.11ac access point to allocate radio resources to communicate with more than one downstream client at the same time. 802.11ax (still in the draft process) provides an improvement to allow MU-MIMO in both downstream and upstream directions.