In plain words
One who does not follow here the wheel thus set in motion, living sinfully and delighting in the senses, lives in vain, Partha.
Word for word
He who here does not keep turning the wheel thus set in motion, whose life is sin, delighting in the senses, he lives in vain, O Pārtha.
The commentators
Bhagavadgītābhāṣyam
एवम् इत्थम् ईश्वरेण वेदयज्ञपूर्वकं जगच्चक्रं प्रवर्तितं न अनुवर्तयति इह लोके यः कर्मणि अधिकृतः सन् अघायुः अघं पापम् आयुः जीवनं यस्य सः अघायुः, पापजीवनः इति यावत् । इन्द्रियारामः इन्द्रियैः आरामः आरमणम् आक्रीडा विषयेषु यस्य सः इन्द्रियारामः मोघं वृथा हे पार्थ, स जीवति ॥
तस्मात् अज्ञेन अधिकृतेन कर्तव्यमेव कर्मेति प्रकरणार्थः । प्राक् आत्मज्ञाननिष्ठायोग्यताप्राप्तेः तादर्थ्येन कर्मयोगानुष्ठानम् अधिकृतेन अनात्मज्ञेन कर्तव्यमेवेत्येतत् ‘न कर्मणामनारम्भात्’(भ. गी. ३ । ४) इत्यत आरभ्य ‘शरीरयात्रापि च ते न प्रसिध्येदकर्मणः’(भ. गी. ३ । ८) इत्येवमन्तेन प्रतिपाद्य, ‘यज्ञार्थात् कर्मणोऽन्यत्र’(भ. गी. ३ । ९) इत्यादिना ‘मोघं पार्थ स जीवति’(भ. गी. ३ । १६) इत्येवमन्तेनापि ग्रन्थेन प्रासङ्गिकम् अधिकृतस्य अनात्मविदः कर्मानुष्ठाने बहु कारणमुक्तम् । तदकरणे च दोषसङ्कीर्तनं कृतम् ॥ १६ ॥
In plain words
'Thus, in this way' — whoever is qualified to act, but fails to keep turning, here in this world, the very wheel of the world the Lord himself set in motion, grounded in the Veda and sacrifice — such a person is 'aghāyuḥ', one whose whole life is sin, one whose living amounts to nothing but sin. That's simply what it means. And 'indriyārāmaḥ' means: someone whose entire delight, whose whole play and enjoyment, is confined to the senses and their objects — that is what it is to delight in the senses. Such a person, Pārtha, lives in vain — utterly, pointlessly.
So the gist of this whole section is this: action really must be performed by the person who is qualified for it but does not yet know the Self. More precisely: before someone becomes fit for the discipline of Self-knowledge, practicing karma-yoga — precisely in order to reach that fitness — really is obligatory for such a qualified but not-yet-Self-realized person. This is exactly what has been established, from the words 'not through refusing to undertake action' (BG 3.4) all the way through to 'even your body's own upkeep would fail without action' (BG 3.8). And then, in the passage running from 'apart from action done for sacrifice' (BG 3.9) all the way through to 'he lives in vain, Pārtha' (BG 3.16), a great deal of supporting reasoning has been given, in passing, for why someone in this position should perform action. And alongside all that, the faults of failing to act have also been laid out in full.
Close to the Sanskrit
'Thus', [i.e.] 'in this way' — whoever, being qualified in [respect of] action, does not keep turning, here in this world, the wheel of the world, set in motion by the Lord, preceded by the Veda and sacrifice — [such a one is] 'aghāyuḥ' [i.e.] one whose life [is] sin — one whose living is sin — that much [is the meaning]. 'Indriyārāmaḥ' [means]: whose delight — [i.e.] enjoyment, [i.e.] play — is by the senses, in [their] objects — [such a one is] 'delighting in the senses'; in vain, uselessly, O Pārtha, he lives.
Therefore, action is indeed to be performed by the ignorant one who is qualified [for it] — this is the purport of the section. That, prior to the attainment of fitness for the discipline of Self-knowledge, the practice of karma-yoga, for that very purpose, is indeed to be performed by the qualified one who does not [yet] know the Self — this [point], beginning from [the words] 'not through the non-undertaking of actions' (BG 3.4), and having been established through [the passage] ending thus, with [the words] 'even the maintenance of the body would not be accomplished for you without action' (BG 3.8); and, by the passage beginning with [the words] 'other than from action for the sake of sacrifice' (BG 3.9), and ending thus, likewise, with [the words] 'in vain, Pārtha, he lives' (BG 3.16), much incidental reasoning has been stated concerning the performance of action by the qualified one who does not know the Self. And, regarding the non-performance of that [action], the enumeration of its faults has been made.