Changing PHP version to PHP 7.1 in Tools&Settings > PHP Settings does not have any effect on a system PHP by OS vendor that still reports PHP 5.4 version:
# php -v
PHP 5.4.16 (cli) (built: Oct 11 2016 14:51:00)
Copyright (c) 1997-2013 The PHP Group
Zend Engine v2.4.0, Copyright (c) 1998-2013 Zend Technologies
with the ionCube PHP Loader (enabled) + Intrusion Protection from ioncube24.com (unconfigured) v5.0.18, Copyright (c) 2002-2015, by ionCube Ltd.
PHP to 7.1 is required for integrating Plesk with pteradoctyl game panel that supports PHP 7.1 only.
PHP versions that can be selected in Tools&Settings > PHP Settings are not responsible for managing system PHP: this menu is intended for controlling what PHP settings and versions Plesk customers can manage. So versions available in Tools&Settings > PHP Settings are for using on a domain level only. See Plesk Administrator Guide for more details.
Plesk interface does not allow managing system PHP.
System PHP version should not be changed/upgraded as Plesk uses it. Do not upgrade system PHP version as this is not supported by Plesk: Plesk may be broken.
To make pteradoctyl game panel work with PHP 7.1, use domain's PHP instead of system PHP:
# /opt/plesk/php/7.1/bin/php -v
PHP 7.1.9 (cli) (built: Sep 1 2017 16:52:25) ( NTS )
Copyright (c) 1997-2017 The PHP Group
Zend Engine v3.1.0, Copyright (c) 1998-2017 Zend Technologies
with Zend OPcache v7.1.9, Copyright (c) 1999-2017, by Zend Technologies
pteradoctyl game panel should be installed on a domain level and PHP for a domain should be set to PHP 7.1 in Domains > example.com > PHP Settings
NOTE: pteradoctyl game panel is not supported in Plesk, so integration should be done by the server administrator side.